Sauté Sausage: In a large pot or Dutch oven, heat olive oil over medium heat. Add sliced smoked sausage and cook until lightly browned. Remove and set aside.
Cook Aromatics: In the same pot, add onions, carrots, and celery. Sauté for 5–6 minutes until softened. Add garlic and cook for 1 minute.
Add Broth and Seasonings: Pour in broth, diced tomatoes (if using), smoked paprika, thyme, bay leaves, salt, and pepper. Bring to a boil.
Simmer Soup: Add cabbage and browned sausage back to the pot. Reduce heat to low and simmer for 20–25 minutes until cabbage is tender.
Adjust Flavor: Taste and adjust seasoning with additional salt, pepper, or smoked paprika if needed. Remove bay leaves before serving.
Serve: Ladle soup into bowls and garnish with chopped parsley or chives. Serve hot with crusty bread or rolls.