Heat a large skillet over medium-high heat; add the sausage and cook 6–7 minutes, breaking it into bite-size pieces, until browned and cooked through.

Transfer sausage to a plate with a slotted spoon, leaving about 2 tablespoons of fat in the pan; discard any extra grease.

Reduce heat to medium; add the sliced onion and cook 4–5 minutes, stirring occasionally, until softened and lightly caramelized.

Stir in the minced garlic and cook 30 seconds until fragrant.

Add the chopped cabbage, tossing to coat with the fat and aromatics; cook 2 minutes to let the edges begin to brown.

Return the sausage to the skillet; season with salt, black pepper, paprika, and caraway seeds (if using), stirring well to combine.

Pour in the chicken broth; bring to a gentle simmer over medium heat, then reduce heat to medium-low.

Cover and cook 8–10 minutes until the cabbage is tender but still slightly crisp, stirring once halfway through.

Remove the lid, stir in the butter until melted and incorporated, taste and adjust seasoning, and serve hot.