Brown the sausage. Heat olive oil in a large stockpot over medium-high heat. Add the Italian sausage and cook, breaking it up with a wooden spoon, until browned and cooked through, about 6–7 minutes. Use a slotted spoon to transfer the sausage to a plate and leave any drippings in the pot.
Sauté aromatics. Add the onion to the pot, season lightly with salt and pepper, and sauté for 4–5 minutes until softened. Stir in the garlic, crushed red pepper flakes, and tomato paste and cook for 1–2 minutes more, stirring often, until fragrant and slightly caramelized.
Add cabbage. Stir in the coleslaw mix and cook for 3–4 minutes, tossing occasionally, until the cabbage begins to wilt.
Simmer. Pour in the chicken stock and return the sausage to the pot. Stir to combine, then bring the soup to a simmer.
Cook the orzo. Add the orzo and cook, stirring occasionally, for 8–10 minutes or until the pasta is just al dente.
Finish. Remove the pot from the heat. Taste and adjust seasoning with additional salt, pepper, and lemon juice if needed.
Serve. Ladle the soup into bowls, sprinkle with extra Parmesan, and enjoy!