Add the cheese tortellini to a large pot of boiling salted water and cook according to the package instructions until al dente (about 3–6 minutes). Before draining, carefully reserve 1 cup of the pasta water. Drain the tortellini and set it aside along with the reserved pasta water.
Heat oil in a medium Dutch oven over medium heat. Once hot, add the diced onion and cook until softened, about 3–5 minutes. Add the minced garlic and cook for 1 more minute, stirring frequently to prevent burning.
Add the mild Italian sausage to the pot, breaking it up with a spatula as it cooks. Stir and cook until the sausage is browned and no longer pink, about 8–10 minutes.
Stir in the tomato paste, diced tomatoes with their juices, Italian seasoning, kosher salt, and freshly cracked black pepper. Mix well to combine, ensuring the sausage and tomato paste are fully incorporated.
Add the softened cream cheese, chicken broth, heavy whipping cream, and grated Parmesan cheese to the pot. Stir continuously until the cream cheese and Parmesan are fully melted and the mixture is smooth, about 10 minutes.
Add the cooked tortellini to the pot, stirring to combine with the creamy sausage mixture. If the soup is too thick, slowly add the reserved pasta water, starting with ½ cup, until you reach your desired consistency. Use the full 1 cup if needed.
Garnish with freshly chopped parsley and extra grated Parmesan cheese before serving.