Heat olive oil in a large nonstick skillet over medium high and add kielbasa. Let cook for a minute or so then stir and cook for a few more minutes until kielbasa is browned. Remove to a plate.
In the same pan , add the cabbage, garlic, onion sugar, salt, and pepper. Stir to combine and cook for about 9-10 minutes, stirring about every 3 minutes. Cook until cabbage is cooked to the softness you like.
Add in the apple cider vinegar and mustard; add the kielbasa back to the pan and cook for another 3 minutes to heat through. Taste and adjust seasoning, if necessary.
Serve over noodles mashed potatoes or as we like it on it's own with a salad.