Cook the pasta: Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain and set aside.
Brown the butter: In a large skillet over medium heat, melt the butter. Continue cooking, swirling occasionally, until it begins to foam and turns golden brown with a nutty aroma (about 4–5 minutes).
Add sage and garlic: Add chopped sage and minced garlic to the browned butter. Sauté for 30–60 seconds until fragrant but not burned.
Stir in pumpkin purée: Reduce the heat to low and stir in the pumpkin purée. Mix well to combine with the butter and sage mixture.
Add cream and seasonings: Slowly pour in the heavy cream while whisking to create a smooth sauce. Add Parmesan, nutmeg, salt, and pepper. Stir until the cheese melts and the sauce thickens slightly.
Toss pasta in the sauce: Add cooked pasta directly into the sauce, tossing to coat. Add a bit of reserved pasta water as needed to reach desired consistency.
Add lemon juice (optional): For brightness, stir in a splash of lemon juice before serving.
Garnish and serve: Plate the pasta and top with additional Parmesan, crispy sage leaves, and a drizzle of brown butter if desired.