Get a large pot of salted water going over high heat.
Heat the olive oil in a large deep skillet or Dutch oven over medium-high. Add the sausage and cook 5-6 minutes, breaking it up, until browned with crispy edges. This develops a lot of flavor. Pour off excess fat, but leave about 2 tablespoons in the pan.
Add the onion and cook 3 minutes, then the garlic for 1 minute.
Push everything to the sides of the pan. Add the tomato paste and Calabrian chili paste to the center and toast 1-2 minutes, until the tomato paste darkens, then stir through.
Pour in the wine and scrape up the browned bits. Cook 1-2 minutes until mostly reduced.
Add the crushed tomatoes, Italian seasoning, and red pepper flakes. Bring to a low boil, then simmer 15-20 minutes, stirring now and then. Season with salt and pepper at the end.
While the sauce is simmering, add the pasta and cook it 1 minute shy of the package time.
Reserve 1 cup pasta water, then drain. Add the pasta straight into the sauce with a good splash of the pasta water. Toss over medium heat 2 minutes so the pasta finishes in the sauce. The starch will thicken the sauce. Add more pasta water if it needs loosening.
Remove from heat and stir in the butter, then the pecorino, then the basil. For a creamy version, stir in 1/3 cup heavy cream at this point, before the basil. Serve with more cheese.