Place a large skillet over medium-high heat and let it warm for a minute. Add the sausage and cook for 5 to 7 minutes, breaking it into small pieces with your wooden spoon as it cooks until it's browned throughout and no pink remains inside.

Once the sausage is cooked through, use a slotted spoon to transfer it to a clean plate, leaving the rendered fat in the pan.

Add the diced onion to the pan with the sausage fat and cook for 3 to 4 minutes, stirring occasionally, until the onion turns translucent and slightly golden.

Stir in the minced garlic, salt, pepper, and smoked paprika and cook for about 30 seconds, stirring constantly.

Add the chopped cabbage to the pan, stirring to coat it with the fat and spices. Pour in the chicken broth and stir everything together, then cook uncovered for 8 to 10 minutes, stirring occasionally, until the cabbage softens and becomes tender.

Once the cabbage is tender, add the cooked sausage back into the pan and stir well to combine. Let everything cook together for 1 to 2 minutes so the flavors marry.

Drizzle the balsamic vinegar over the pan and stir to distribute evenly.

Taste the dish and add more salt, pepper, or red pepper flakes if needed. Serve hot from the pan.