Cook the noodles by boiling a large pot of salted water. Add the lasagna noodles and cook until al dente, about 8-10 minutes. Drain and lay noodles flat to cool.

In a large mixing bowl, combine mashed butternut squash, ricotta, Parmesan, egg, sage, salt, and pepper. Mix until smooth and set aside.

In a saucepan, melt butter over medium heat. Whisk in flour until golden, then add warm milk gradually while whisking until sauce thickens. Stir in Parmesan, nutmeg, cayenne, salt, and pepper.

Preheat oven to 375°F (190°C). Spread butternut squash filling on each lasagna noodle, sprinkle with mozzarella, and roll up. Place seam-side down in a baking dish.

Spread half of the béchamel sauce on the bottom of the dish, place the rolls, pour remaining sauce on top, and sprinkle with extra mozzarella. Bake for 30 minutes until bubbly and golden.

Let cool for a few minutes, garnish with sage leaves, and serve warm.