Fill a pasta pot half full with water and season with 2 teaspoons kosher salt. Bring the water to a boil, add the pasta and cook to just shy of al dente (about 2 minutes shy of package instructions). Reserve 3/4 cup of pasta water, drain the pasta in a colander, and set aside.

Preheat an oven to 425 F. Heat a large, oven-safe skillet over medium heat. Add the sausage and brown for 5 minutes, breaking the sausage up into pieces until no longer pink and some of the fat has rendered out. Add the chopped sage and cook for 2 more minutes. Using a slotted spoon, transfer the sausage and sage to a bowl and set aside.

Melt the butter in the skillet used to cook the sausage and add the onions and garlic. Cook for 2-3 minutes until the onions have softened. Add the pumpkin puree, pasta water, and half and half and bring to a simmer. Add the parmesan cheese and stir until completely melted. Season to taste with salt and pepper, but remember that the pasta water has salt and so does the parmesan.

Add the pasta and sausage to the skillet with the sauce and toss until all the pasta is coated with sauce and the sausage is evenly distributed. Top with the pieces of fresh mozzarella, cover with foil, and transfer to the oven to bake for 15 minutes.

Change the oven settings from bake to broil on high and remove the foil. Broil for 2-3 minutes until the mozzarella is bubbly and browned in spots. Remove from the oven and top with fresh basil and more parmesan. Serve right away.