Preheat oven to 400°F. Remove the stem of the squash and slice it in half lengthwise. Discard the seeds. Drizzle the cut sides with 1 tbsp olive oil and set the cut side down on a parchment-lined baking sheet.
Slice off the stem and about ¼-inch from the top of the head of garlic, exposing all the cloves. Place in the center of a square of aluminum foil. Fold up the corners of the foil and tightly pinch to create a packet.
Place both the squash and garlic in the preheated oven. Cook the squash until tender and softened, 30-40 minutes. Cook the garlic until golden brown and soft, 40 minutes.
Once the squash is done cooking, start the pasta. Bring 4 quarts of water to a boil and add 2 tbsp salt. Pour in the pasta and cook until al dente, or when the pasta still has a slight bite. Paccheri pasta will be about 12-15 minutes. Once al dente, remove from the water until ready to add to the sauce.
While the pasta is cooking, prepare the sauce. In a 6-quart Dutch oven, add 1 tbsp olive oil over medium heat. Add the sausage and spread to an even layer. Sauté until browned on both sides, 6-8 minutes. Remove the sausage from the Dutch oven and add the onion, salt, and garlic. Sauté until softened, 4-6 minutes. Add the red pepper flakes and sage. Then add the tomato paste. Stir and cook the tomato paste until darker in color and just beginning to stick to the bottom of the Dutch oven.
Add the scooped out squash and 1 cup of pasta cooking water. Use a potato masher if the squash needs to be further mashed. Turn the heat to low. Stir until smooth.
Add the pasta and stir until it is all coated in sauce. Add the reserved sausage and Parmesan cheese. Stir and serve.