Bring a large pot of salted water to a boil. Cook the rigatoni according to the package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta and set it aside.
Heat the olive oil in a large, deep skillet over medium-high heat. Add the beef sausage and cook until browned and fully cooked, breaking it into bite-sized pieces as it cooks.
Transfer the cooked sausage to a plate lined with paper towels. Leave the flavorful drippings in the skillet.
Add the minced garlic and shallot to the skillet. Sauté for 3 to 5 minutes, until softened and fragrant.
Add 3/4 cup chicken broth and scrape the bottom of the skillet to loosen any browned bits. Simmer for about 2 minutes.
Stir in the pumpkin puree, remaining broth, and 1 tablespoon of chopped sage.
Return the beef sausage to the skillet and reduce the heat to medium-low.
Stir in the heavy cream, nutmeg, cinnamon, and cayenne. Season with salt and black pepper.
Let the sauce simmer for 5 to 10 minutes, stirring occasionally, until it becomes creamy and slightly thickened.
Add the cooked pasta and gently toss until thoroughly coated. If the sauce is too thick, add reserved pasta water a little at a time until it reaches your preferred consistency.
Taste and adjust the seasoning. Serve the Pumpkin Sausage Pasta immediately with shaved Parmesan and the remaining fresh sage.