Step 1

Prepare the vegetables. Peel and finely chop 1/2 medium yellow onion. Peel 1 medium carrot. Cut the carrot and 1 celery stalk into 1/4-inch dice. Measure out 2 cups canned whole tomatoes and their juices, and coarsely chop the tomatoes.

Step 2

Cook the vegetables. Put the onion, carrot, celery, 3 tablespoons unsalted butter, and 2 tablespoons extra-virgin olive oil in a large, heavy bottomed saucepan and place over medium-high heat. Sauté, stirring occasionally, until the vegetables have lightly browned, about 10 minutes.

Step 3

Add the beef, wine, and milk. Add 12 ounces ground beef and break it up with a wooden spoon. Cook until the beef is cooked through and no longer pink. Add 1/2 cup dry white wine and cook, stirring occasionally, until almost half the liquid has evaporated. Add 1/2 cup whole milk and 1/8 teaspoon ground nutmeg and cook, stirring occasionally, until half the milk has evaporated.

Step 4

Add the tomatoes. Add the tomatoes and their juices, and 1 1/4 teaspoons fine salt. Once the tomatoes have started bubbling, turn the heat down very low so that the sauce is barely simmering. Cook uncovered, stirring every 15 to 20 minutes, for 3 1/2 hours. (This is a good time to make the pasta.) If all the liquid evaporates before the cooking time is up, add water in 1/2-cup increments as needed. Make sure all the liquid has evaporated before removing the sauce from the heat.

Step 5

Set up the flour and eggs. Pour 2 1/4 cups unbleached all-purpose flour in a mound in the center of your work counter. Make a well into which the eggs will fit comfortably. To avoid the possibility that the eggs will overflow, it is better to make the well a little too wide than too small.

Step 6

Mix in the eggs with a fork. Break 3 large eggs into the center of the well. Use a fork to beat the eggs until the yolks and the whites are thoroughly blended together. Mix a little flour into the eggs with the fork. Continue adding flour until the mixture thickens enough to cling to the fork when you lift it. Set the fork aside, using your fingers to squeeze the dough attached to the fork back into the well.

Step 7

Mix with your hands. Push about 1/4 cup of flour to the side, then use your hands to bring the rest into the center. Mix together with your hands to begin forming a dough. The dough should feel moist but not sticky when you plunge a finger into it. If it feels sticky, add a little more flour.

Step 8

Wrap the dough. Wrap the dough in plastic wrap. Scrape off any bits of dough that have stuck to the counter and wash your hands. Reserve any remaining flour and set aside.

Step 9

Knead the dough until smooth. Unwrap the dough and begin kneading it. Think of stretching the dough rather than compressing it, using the heel of your palm and pushing away from you. Knead until the dough feels homogeneous and smooth, 5 to 6 minutes. If it seems to stick to your hand or the counter, add a little more flour. On the other hand, if it feels too hard to knead, you may have added too much flour. Try wetting your hands and kneading the moisture in. If that does not seem to help, it’s probably easier and faster to start over. Adding flour during the kneading process may increase the time, since the further along you are, the longer it takes for the flour to get incorporated.

Step 10

Rest the dough. When you have kneaded the dough sufficiently, wrap it in plastic wrap again and let it rest for at least 15 minutes or up to 3 hours. Never refrigerate or freeze pasta dough. As the dough rests, the gluten in the flour will relax, making it much easier to roll. (This is a good time to make the béchamel.)

Step 11

Unwrap and cut the dough. Unwrap the dough and knead it a few times to incorporate the moisture that inevitably rises to the surface. The surface of the dough at this point should feel silky smooth (a baby’s bottom is what it is traditionally compared to). Cut the dough into 3 pieces. Wrap 2 of the pieces back in the plastic wrap.

Step 12

Roll out the dough into sheets. Flatten the remaining piece of dough as best you can with your hands, then put it through the rollers of a pasta rolling machine set at the thickest setting. Fold the dough into thirds like a letter, and put it through the rollers again with the folds perpendicular to the rollers. Fold the dough in half and put it through one more time, again with the folds perpendicular to the rollers. Lay the dough sheet on a clean kitchen towel and repeat the procedure with the other two pieces.

Step 13

Roll the sheets again thinly. When all the pieces have been through the machine at the widest setting, adjust the rollers down one notch and put each sheet through once. Repeat, going down one notch at a time, until you reach the next to last setting. Cut each sheet of pasta in half crosswise, then put each piece through the machine at the thinnest setting. Cut each sheet in half crosswise again so that you have 12 total pieces.

Step 14

Heat the milk and make the roux. Place 2 cups whole milk in a small saucepan over medium heat and heat until steam is released when the milk is stirred. Meanwhile, melt 4 tablespoons unsalted butter in a 2-quart saucepan over medium-low heat. Add 1/4 cup all-purpose flour and whisk until the mixture is smooth. Cook, whisking constantly, for about 1 minute, then remove from the heat. Do not let the flour brown.

Step 15

Add the warmed milk to the roux. When the milk is hot, transfer it to a heatproof measuring cup or pitcher with a spout. Return the flour mixture to medium heat and begin adding the hot milk, very slowly at first, mixing with the whisk. Do not be concerned if the mixture becomes quite thick at first. Continue adding the milk slowly while mixing with the whisk. As the consistency becomes thinner, you can add the milk more rapidly until all of it has been mixed in.

Step 16

Add the salt and cook until thickened. Add 1/2 teaspoon fine salt and cook over medium heat, whisking constantly, until the sauce begins to thicken, 10 to 15 minutes. The sauce is done when it coats the whisk thickly.

Step 17

Bring water to a boil and make an ice bath. Fill a large pot for the pasta with at least 6 quarts of water, place over high heat, and bring to a boil. Fill a large bowl halfway with ice and water and keep it close to the pot of water on the stove.

Step 18

Cook the pasta. Add 2 tablespoons fine salt to the boiling water and put in 4 of the pasta sheets. Cook for 1 minute, then lift the pasta out of the water and place it in the bowl of ice water. I find it easiest to do this with a pair of tongs, but you have to be careful not to rip the pasta. Swish the pasta sheets in the water, then lay them flat on dry kitchen towels. Repeat with the remaining 8 pasta sheets in two more batches.

Step 19

Heat the oven. Preheat the oven to 425°F.

Step 20

Coat the bottom of the baking dish and make the filling. Spread a thin coating of béchamel on the bottom of an 8 x 11 1/2-inch rectangular baking dish. Mix the remaining béchamel with the bolognese sauce and 1/2 cup of the Parmigiano-Reggiano to make the filling.

Step 21

Add a layer of pasta. Use the bottom of the baking dish to determine the length of pasta needed to cover it completely and cut a piece of pasta that you’ll use as a template for all the layers. Place a sheet of pasta on the bottom of the pan, filling in with smaller strips any area that the sheet does not cover.

Step 22

Assemble the lasagne. Spread a thin coating of the filling over the pasta sheet, then cover with another sheet of pasta. Continue until you have 7 or more layers of pasta and filling, saving a little filling to cover the top layer. Cover the top layer of pasta with the remaining filling.

Step 23

Sprinkle with cheese and dot with butter. Sprinkle the remaining 1/4 cup Parmigiano-Reggiano over the top and dot with 1 tablespoon unsalted butter broken up into a few pieces.

Step 24

Bake the lasagne. Bake until the top has lightly browned, 20 to 25 minutes. Take the lasagne out of the oven and let it rest for 5 minutes before serving.