Heat the oil in a skillet over medium-high heat and brown the sausage, breaking it into bite-size pieces, 7 to 8 minutes.
Add the onion and cook until soft, 4 minutes, then stir in the garlic for 30 seconds.
Transfer the mixture to a 6-quart slow cooker and stir in the pumpkin, tomatoes, broth, sage, salt and pepper.
Cover and cook on low for 5 to 6 hours until the sauce darkens slightly and the onion disappears into it.
Stir in the cream and keep the cooker on warm while boiling the rigatoni in salted water until just tender.
Drain the pasta, fold it and 3/4 cup Parmesan into the sauce and let it stand for 5 minutes.
Serve with the remaining 1/4 cup Parmesan over the top.