A whole head of cabbage is cooked with brown sugar, Creole seasoning, and cider vinegar in the same pot as the kielbasa until it strikes the perfect balance between crisp and tender.
Melt 1 tablespoon butter and oil in a large pot or 1 1/2-quart braiser over medium heat. Add sausages and cook, flipping once, until golden brown, about 6 minutes. Transfer to a plate.
Add remaining 1 tablespoon butter to pot, along with onion, brown sugar, and Creole seasoning. Cook, stirring occasionally, until onion is translucent, 6 to 8 minutes. Stir in half of cabbage and vinegar; season with salt. As mixture begins to reduce in volume, add remaining cabbage; season with salt. Cover and cook, stirring a few times, until cabbage is softened and wilted but still has a slight crunch, about 25 minutes. Season with salt and pepper to taste.
Nestle sausages into cabbage and cook just until warmed through, about 2 minutes. Cut sausages into 1/2-inch-thick pieces; serve with cabbage and mustard, if desired.