Preheat the oven to 400°. On a large rimmed baking sheet, drizzle the squash with 2 tablespoons of oil and toss. Arrange in an even layer and season with salt, pepper and nutmeg. Bake for about 30 minutes, until just tender. Add the chopped sage and toss.
Meanwhile, put the pecans in a pie plate and bake for about 4 minutes, until toasted.
In a large skillet, melt the butter. Add the whole sage leaves and cook over moderate heat, turning once, until crisp, 2 minutes. Transfer the leaves to a plate and pour the butter into a bowl. Add the remaining 1 tablespoon of oil and the sausage to the skillet and cook over moderately high heat, breaking up the sausage, until no pink remains, 7 minutes.
In a large pot of boiling salted water, cook the pasta until al dente. Drain, reserving 1 cup of the cooking water. Return the pasta to the pot. Add the sausage and melted butter and gradually stir in the cooking water over moderate heat. Gently fold in the squash, pecans and the 1/4 cup of cheese. Season with salt and pepper and transfer to a bowl. Scatter the sage on top and serve with more cheese.