Bring a large pot of salted water to a boil. Cook the pasta until al dente according to package directions. Reserve 1 cup pasta water, then drain the pasta. Do not rinse.
While the pasta cooks, heat olive oil in a large deep skillet over medium-high heat. Add the Italian sausage and cook for 6 to 8 minutes, breaking it into crumbles, until browned and fully cooked.
If needed, carefully drain excess grease, leaving about 1 tablespoon in the skillet. Add the diced onion, if using, and cook for 3 to 4 minutes until softened.
Add garlic, sage, Italian seasoning, black pepper, red pepper flakes, and nutmeg, if using. Stir for 30 seconds, until fragrant.
Reduce the heat to medium-low. Add pumpkin purée, broth, and heavy cream. Stir until smooth.
Simmer gently for 3 to 4 minutes. Do not boil vigorously.
Stir in Parmesan cheese until melted and smooth. Add ¼ cup reserved pasta water and stir. Add more pasta water as needed to create a silky sauce.
Add the drained pasta and cooked sausage to the skillet. Toss until fully coated in sauce.
Add spinach, if using, and toss for 1 to 2 minutes until wilted. Stir in lemon juice, if using.
Taste and add salt, black pepper, or red pepper flakes as needed. Add more pasta water or broth if the sauce becomes too thick.
Serve immediately with extra Parmesan, parsley, crispy sage, bacon, walnuts, or red pepper flakes.