Butternut Squash Agnolotti

Name: Butternut Squash Agnolotti
Ingredients: ½ butternut squash (about 1 pound), peeled, seeded, cut into ½-inch pieces; 1 shallot, unpeeled; 1 garlic clove, unpeeled; 3 tablespoons olive oil; 2 sprigs thyme; Pinch of red pepper flakes (optional); 20 sage leaves, divided; Kosher salt, freshly ground pepper; ½ cup walnuts; 2 tablespoons grated Parmesan, plus more for serving; 2 tablespoons mascarpone, crème fraîche, or sour cream; 1 teaspoon fresh lemon juice; Cornmeal or semolina flour (for dusting); Fresh Pasta Dough; 6 tablespoons unsalted butter; A pastry bag with a ¼-inch tip; a fluted pasta cutter