Bring a large pot of salted water to a boil. Add the jumbo shells and cook according to the package directions until they are al dente. Drain the pasta and rinse with cool water to stop the cooking process and prevent them from sticking together.
In a large mixing bowl, combine the pumpkin puree, ricotta cheese, mozzarella, Parmesan cheese, beaten egg, minced garlic, nutmeg, salt, and pepper. Stir everything together until the mixture is smooth and well combined.
Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish. Take a cooked shell and fill it with about 2 tablespoons of the pumpkin mixture. Place the stuffed shell into the prepared baking dish. Repeat this process until all shells are filled.
Cover the baking dish with aluminum foil. Bake in the preheated oven for 20 minutes. Remove the foil and bake for an additional 5 to 10 minutes, or until the cheese is melted and the shells are heated through.
While the shells are baking, place the butter in a medium skillet over medium heat. Melt the butter and continue cooking until it begins to turn a golden brown color and smells nutty. Add the fresh sage leaves and fry them for about 1 minute until they are crisp. Remove from heat immediately.
Once the shells come out of the oven, drizzle the hot sage butter and the crispy leaves over the top of the shells. Sprinkle with extra Parmesan cheese and serve immediately.