Heat olive oil in a large skillet or Dutch oven over medium heat.
Add sliced sausage and cook for 4 to 5 minutes until browned, then remove and set aside.
In the same pan, cook sliced onion for 3 to 4 minutes until softened.
Add minced garlic and cook for 30 to 60 seconds until fragrant.
Add chopped cabbage and diced potatoes, cooking for 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 as needed to loosen the sauce and help vegetables cook.
Return the browned sausage to the pan, bring to a gentle simmer, cover, and cook for 15 to 20 minutes until potatoes are tender and cabbage is soft.
Stir occasionally and add more broth if sauce becomes too thick.
Serve hot with chopped fresh basil or parsley and grated Parmesan cheese if desired.