Step 1

Make the bechamel: In a medium (3-quart) saucepan over medium-high heat, melt the butter. Whisk in the flour until the mixture looks pasty but smooth, and cook, stirring constantly, until it smells toasty and is light golden brown, 3 to 6 minutes. Whisking constantly, slowly pour in the milk. Take care, as the milk may sputter and splatter. Add the nutmeg, and continue whisking until the sauce is smooth and thick enough for the whisk to leave a visible trail and coat the back of a spoon without immediately running off, 3 to 4 minutes. Remove from the heat. Taste, and season with the salt and a few grinds of pepper. Taste again, and season with more salt, if needed. Let cool for 10 to 15 minutes. (Do not let the sauce cool completely at this stage.)

Step 2

In a small bowl, beat the eggs until frothy. Whisk the eggs, yogurt and cheese into the mixture in the saucepan until well combined.

Step 3

Make the meat sauce: In a large (12-inch) skillet over medium-high heat, heat the oil until shimmering. Add the beef and a generous pinch of salt, and cook, breaking up the meat into nubbins with a wooden spoon, until brown, 3 to 5 minutes. (The beef will not be cooked through.) If there is a lot of grease at the bottom of the pan, discard all but about 2 tablespoons. Add the onion, carrots, celery and another pinch of salt, and cook, stirring occasionally, until the vegetables soften and the onion just begins to brown, 5 to 7 minutes. Stir in the tomato paste, garlic, cinnamon, allspice and nutmeg, and cook until very fragrant, about 30 seconds. Stir in the tomatoes and wine, if using. Cover the skillet, reduce the heat to low, and simmer until the sauce thickens, 10 to 15 minutes.

Step 4

Assemble the pastitsio: While the sauce is cooking, bring a large pot of water to a boil. Lightly grease a 9-by-13-inch ovenproof dish that has at least 2-inch-high sides with butter. Position a rack in the middle of the oven and preheat to 375 degrees.

Step 5

Add the pasta to the boiling water and cook 3 minutes less than the package instructions for al dente. Drain, and return the pasta to the pot. Add 1/3 cup (1 ounce) of the cheese, 1 cup of the bechamel and the butter, and stir gently to combine. Transfer the pasta to the prepared baking dish, and use a flexible spatula to spread it into an even, compact layer.

Step 6

Spread the meat sauce evenly over the pasta, then pour the remaining bechamel over, spreading it from edge to edge. (If your dish isn’t deep enough, you may need to hold some bechamel back. Do not overfill the pan, because it may bubble over in the oven.) Sprinkle with the remaining 1/3 cup (1 ounce) of cheese. Bake, uncovered, for 40 minutes, or until the top is speckled golden brown.

Step 7

Remove the pastitsio from the oven, and let rest for at least 15 minutes before slicing and serving.