Heat olive oil in a large pot over medium heat. Add onion and cook for 5 minutes until softened.
Stir in garlic, oregano, and red pepper. Cook for 15 seconds until fragrant. Add Italian sausage, breaking it up, and cook for 15 minutes until no longer pink. Stir in tomato paste.
Add chicken broth, tomato puree, sun-dried tomatoes, and 1 teaspoon salt. Bring to a simmer and cook for 15 minutes.
Stir in tortellini and kale. Simmer for 3-5 minutes until tortellini is tender and kale is wilted. Remove from heat.
Stir in Parmesan cheese. Serve immediately with extra cheese on the side.