A creamy, cheesy lasagna perfect for the cooler months.
Preheat oven to 400°F with rack in middle position.
Toss together squash, olive oil, and cayenne pepper on a large rimmed baking sheet; spread into an even layer. Bake until tender, about 35 minutes.
Meanwhile, cook butter in a small saucepan over medium until butter browns and has a nutty aroma, 4 to 5 minutes. Remove from heat.
Process ricotta, Parmesan, eggs, and salt in a food processor until well combined, about 45 seconds. Transfer cheese mixture to a medium bowl, and stir in spinach and chopped sage; set aside. Clean food processor bowl.
Add cooked squash to the clean food processor bowl. Process until smooth, about 1 minute, stopping to scrape sides halfway through. Add brown butter to squash, and pulse until combined, about 10 pulses. Transfer to a bowl.
Lightly grease a 13- x 9-inch baking dish with butter. Spread 3/4 cup of the squash puree in bottom of prepared dish. Arrange 3 noodles on top. Spread 1 3/4 cups of the ricotta mixture over noodles, top with 3/4 cup of the squash puree, and sprinkle with 1 1/3 cups of the mozzarella. Repeat the layering process twice, beginning with noodles and ending with mozzarella. Cover lasagna with lightly greased aluminum foil.