Step 1

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.

Step 2

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.

Step 3

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.