Prep your ingredients. Slice the sausage into rounds. Core and thinly slice the cabbage. Slice the onion, mince the garlic, and prep the carrot if using. Having everything ready makes the cooking process smooth.

Brown the sausage. Heat a large skillet over medium-high and add 1 tablespoon oil. Add the sausage and cook 3–5 minutes, flipping once, until browned at the edges. Remove to a plate and leave the flavorful fat in the pan.

Soften the aromatics. Add the remaining oil and the onion and carrot. Cook 3–4 minutes until the onion turns translucent. Stir in the garlic and cook 30 seconds until fragrant.

Build the flavor base. Sprinkle in smoked paprika, caraway seeds, and red pepper flakes if using. Stir to coat the vegetables so the spices bloom in the hot fat.

Add the cabbage in batches. Pile in half the cabbage, sprinkle with a pinch of salt and pepper, and toss until it starts to wilt. Add the rest and continue tossing. Don’t worry if the pan is full—it will cook down quickly.

Steam to tenderize. Pour in 1/3 cup broth (add more if needed). Cover the skillet and cook 5–7 minutes, stirring once or twice, until the cabbage is tender but not mushy.

Bring it together. Uncover, return the sausage and any juices to the pan, and add the vinegar and Dijon. Toss everything and cook 2–3 more minutes to let the flavors meld and the liquid reduce slightly.

Taste and adjust. Add more salt, pepper, or vinegar to balance richness. You’re looking for savory, slightly tangy, and a hint of smokiness.

Finish and serve. Sprinkle with chopped parsley and serve hot. It’s great on its own, with crusty bread, over mashed potatoes, or alongside rice or noodles.