Heat your largest skillet over medium-high heat. No need to add oil yet—we'll use the fat from the sausage.
Add the sliced kielbasa to the hot skillet in a single layer. Let it cook undisturbed for 2-3 minutes until it develops a nice brown crust on one side.
Flip the sausage pieces and brown the other side for about 2 minutes. The goal is to render out some of that flavorful fat and create caramelized edges. Once browned, transfer the sausage to a plate, leaving the fat in the pan.
Reduce heat to medium and add the butter or olive oil to the sausage fat. Once melted, add the sliced onions with a pinch of salt.
Cook the onions for about 5 minutes, stirring occasionally, until they begin to soften and turn translucent.
Add the minced garlic and caraway seeds (if using) to the onions. Cook for just 30 seconds until fragrant—don't let the garlic burn.
Stir in the paprika, then immediately add the sliced cabbage. Don't worry if it seems like too much—cabbage cooks down significantly.
Cook the cabbage for about 10 minutes, stirring occasionally. You want it to soften and begin to caramelize in spots. If the pan gets too dry, add a splash of chicken broth or water.
Once the cabbage has wilted down and is tender but still has some texture, add the apple cider vinegar and stir to deglaze the pan, scraping up any browned bits from the bottom—that's pure flavor!
Return the browned kielbasa to the skillet, along with any accumulated juices. Gently fold it into the cabbage mixture.
Cook everything together for another 3-4 minutes until the flavors meld and everything is heated through.
Season with black pepper and adjust salt if needed, remembering that kielbasa is already quite salty.
Garnish with fresh parsley before serving hot.