Ravioli filled with squash and goat cheese and tossed with brown butter makes pasta night the best night.
2 cups cubed butternut squash (from 1 small [about 1 1/2 pounds] squash)
1/8 teaspoon ground nutmeg
1 large garlic clove, smashed
2 tablespoons olive oil, divided
1 teaspoon kosher salt, divided
1/2 teaspoon black pepper, divided
10 large eggs
2 1/3 cups (about 10 ounces) all-purpose flour, plus more as needed
1 ounce goat cheese, crumbled (1/4 cup)
1/2 ounce pecorino Romano cheese, grated with a Microplane grater (about 2 tablespoons), plus more for garnish
1 teaspoon whole milk
3/4 cup roughly chopped walnuts
1/2 cup (4 ounces) unsalted butter
1/4 cup loosely packed fresh sage leaves (from 1 [1/4-ounce] package)
2 cups packed torn kale (from 1 [9-ounce] bunch)
Preheat the oven to 400°F. Toss together the squash, nutmeg, garlic, 1 tablespoon of the oil, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper on a large rimmed baking sheet until evenly coated; spread into a single layer. Bake the squash in the preheated oven until fork-tender, about 35 minutes, stirring once halfway through baking time.
Meanwhile, whisk together 2 whole eggs, 8 egg yolks, and the remaining 1 tablespoon oil in a medium bowl. Reserve the egg whites for another use. (Egg whites may be frozen in an airtight container for up to 1 year.) Place the flour in the bowl of a stand mixer fitted with a dough hook attachment. With the mixer running on low speed, slowly add the egg mixture. Beat until mostly incorporated, 30 to 40 seconds (there will be some loose flour in the bottom of the bowl). Beat on low speed until the dough is smooth and flour is incorporated, 2 to 4 minutes, stopping once or twice to scrape the dough from the hook and press it into the loose flour in the bottom of the bowl. Transfer the dough to a clean work surface, and knead by hand until elastic, 3 to 5 minutes. (Dough should be the consistency of modeling clay.) If the dough is too sticky, sprinkle it with additional flour, 1 teaspoon at a time; if it is dry and cracking, sprinkle with water, a few drops at a time. Wrap the dough in plastic wrap, and let it rest at room temperature at least 30 minutes or up to 2 hours before rolling and shaping.
Transfer the roasted squash to a large bowl; gently mash using a fork or potato masher until it is smooth, about 1 minute. Stir in the goat cheese, pecorino, and milk until evenly combined; you should have about a cup of filling. Set aside, uncovered, until ready to use.
Cut the rested pasta dough into 4 equal pieces, and cover them loosely with plastic wrap. Working with 1 piece at a time, flatten the dough to 1/4-inch thickness, about 5- x 4-inches. Lightly dust with additional flour. Roll the dough, starting on the 5-inch side, once through a pasta machine set on the widest setting. Fold the dough into thirds (like a letter); roll it through the widest setting once more, with the folded edge first. Repeat the folding and rolling process once more. Continue rolling the pasta through the machine at successively narrower settings, twice per setting; the dough should be thin enough to see the outline of your hand. Set the dough aside on a lightly floured work surface, and cover it with a clean kitchen towel. Repeat the process with remaining dough pieces.
Bring a large pot of salted water to a boil over medium-high. Place 1 dough sheet on a floured work surface. Trim the edges to create 1 (24-inch-long) rectangle; cut the dough sheet in half lengthwise (about 2 to 2 3/4 inches wide). Spoon 10 teaspoons of the filling, about 2 fingers apart, in a single row down the center of the dough. Lightly brush water around the filling; cover with the other dough sheet half, and smooth the dough sheet using your fingertips, working around the filling to press any air bubbles out. Press to seal the edges and sides together. Using a fluted or straight pastry cutter or sharp knife, cut between the fillings to create 10 ravioli (2- to 2 1/2-inch squares). Place the ravioli in an even layer on a large rimmed baking sheet dusted with additional flour; cover with a clean kitchen towel. Repeat the process 3 more times using the remaining dough sheets and filling.
Heat the walnuts and butter in a large skillet over medium, stirring occasionally, until the butter is melted, 3 to 5 minutes. Add the sage; cook, stirring constantly, until the butter is light brown and has a nutty aroma, 4 to 5 minutes. Remove from heat.
Add half of the ravioli (20) to boiling water; cook over high until al dente and the ravioli rise to the surface, about 3 minutes. Using a slotted spoon or spider, quickly transfer the ravioli directly to the brown butter in the skillet. Repeat the process with the remaining ravioli.
Return the skillet heat to medium; add the kale and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper; cook, gently tossing occasionally, until the kale is wilted and the ravioli are fully coated, about 2 minutes. Garnish with additional pecorino.
