Heat olive oil in a large skillet or Dutch oven over medium heat.
Add sliced sausage and cook 4 to 5 minutes until browned, then remove and set aside.
In the same pan, sauté onion until softened, about 3 to 4 minutes.
Add minced garlic and cook for 30 to 60 seconds until fragrant.
Add chopped cabbage and diced potatoes, cooking 5 to 7 minutes while stirring occasionally.
Stir in crushed tomatoes, diced tomatoes (if using), tomato paste, basil, oregano, salt, pepper, and paprika.
Pour in broth to loosen the sauce and help vegetables cook.
Return browned sausage to the pan, bring to a gentle simmer, cover, and cook 15 to 20 minutes until potatoes are tender and cabbage is soft.
Stir occasionally, adding more broth if sauce becomes too thick.
Serve hot, garnished with fresh basil or parsley and grated Parmesan if desired.