Butternut Squash Lasagna with Brown Butter and Sage

Name: Butternut Squash Lasagna with Brown Butter and Sage
Ingredients: 2 butternut squashes, peeled and halved crosswise, seeded half reserved for another use; 8 Tbs. (1 stick) (4 oz./125 g) unsalted butter; Kosher salt and freshly ground black pepper; 2 tsp. olive oil; 1 lb. (500 g) spinach, tough stems removed; 1/4 cup (1 1/2 oz./45 g) all-purpose flour; 1 Tbs. chopped fresh sage; 3 1/2 cups (28 fl. oz./875 ml) whole milk; Pinch of cayenne pepper; Pinch of grated nutmeg; 2 1/2 cups (10 oz./310 g) grated mozzarella cheese; 1/4 cup (1 oz./30 g) grated Parmesan cheese