Step 1

Make the agnolotti dough: Add the flour and eggs to the bowl of a food processor. Blend until it’s sandy but holds together when pressed between your fingers, about 30 seconds. Turn out the dough on a floured work surface. It will be crumbly, but once you start kneading, it will all come together. Gather the dough and knead with the heel of your hand until it’s supple and shiny, 4 to 5 minutes. If the dough feels too dry and not springy enough, add a touch of water and continue to knead until it reaches the right consistency. Wrap the dough in plastic wrap and allow it to rest at room temperature for 30 minutes or up to 1 hour. Line a sheet pan with parchment paper and set aside.

Step 2

Make the filling: Preheat the oven to 400 degrees F.

Step 3

Toss the squash and leeks in the oil and sprinkle well with salt and pepper. Spread out on a baking sheet and bake until golden and soft, 12 to 15 minutes. Let cool completely. Put the vegetables in the clean bowl of the food processor, then add the mascarpone and Gorgonzola and puree until smooth. Season with salt and pepper. Assemble a pastry bag with a 3/4-inch round tip. Fill the bag with the squash-leek filling, then set aside.

Step 4

Form the agnolotti: To roll out the pasta, cut the dough into 6 equal pieces. Working with one piece at a time (keep the others covered with plastic wrap), flatten the dough with your palm. Feed the dough through a pasta machine on the widest setting. Fold the dough on either end to create an envelope, then feed through the pasta machine a second time. Fold the dough into an envelope again, then decrease the setting to make it thinner, and run it through again. Repeat this process of folding and running through the pasta machine two times before decreasing the thickness of the machine. Lay the sheets of pasta on a baking sheet as done and cover with a damp towel while you repeat with the remaining pieces of dough.

Step 5

Lay a pasta sheet on a lightly floured board. Brush the edge closest to you with water. Pipe tablespoon-sized mounds of filling in a line in the center of the dough, spacing them about 1-inch apart. Fold over the top portion of the dough to meet the edge that’s been brushed with water. Pinch the dough on either side of each mound of filling to seal the dough and ensure that there are no air pockets. Using a fluted pasta wheel, trim the edge of the dough where it’s folded to create a clean edge. Cut between each mound of filling and pinch in the sides. Transfer the agnolotti to a sheet tray dusted with flour and loosely cover with plastic wrap. Repeat with the remaining dough sheets and filling.

Step 6

Make the sauce: Line a sheet pan with a paper towel and set aside. To a large skillet, add the stick of butter and the garlic and gently melt over medium heat. Add the walnuts and sage leaves. Cook the butter, while slightly browning the garlic and crisping the sage leaves, swirling occasionally, until the milk solids have separated and the butter is nutty and browned, but not burned, 7 to 8 minutes. Remove the garlic and discard; transfer the sage leaves to the sheet pan and let dry. Add the vinegar to the pan and set aside.

Step 7

Cook the agnolotti: Set up a large pot of boiling water and season generously with salt. Add the agnolotti, give it a quick stir and cook for 2 to 3 minutes; they will cook quickly.

Step 8

Transfer the agnolotti with a spider or slotted spoon directly to the pan and toss gently to ensure that they’re fully covered in the brown butter sauce. Divide the agnolotti among the plates. Crush or tear the crispy sage leaves over the pasta and top with pecorino.