Brown the Sausage: Heat 1 Tablespoon of oil in a large skillet over medium heat. Add the sliced 13 ounces kielbasa, sliced into rounds and cook for 4–5 minutes until nicely browned. Remove the sausage from the pan and set aside.
Sauté the Onion: In the same pan, add the remaining 1 Tablespoon of oil, if needed. Add the 1 medium onion, diced and cook for 3–4 minutes until soft and translucent.
Add the Cabbage: Add the chopped 1 small green cabbage to the skillet. There will be a lot - it will wilt down, don't worry! Pour in ¼ cup chicken broth, then cover with a lid.
Let it steam for 8–10 minutes, stirring every now and then, until the cabbage is softened but not mushy.
Combine and Simmer: Stir the browned kielbasa back into the cabbage mixture. Cover again and simmer on low for another 3–4 minutes.
If the cabbage has released a lot of liquid, remove the lid and cook over high heat for a few minutes so the excess can evaporate.
Finish the Dish: Season to taste with salt and freshly ground black pepper. Stir in the 1 Tablespoon apple cider vinegar just before serving for a bright, tangy finish.
Serve: Garnish with chopped fresh parsley, dill or chives