Step 1

Thinly slice 1/2 large red onion if using. Drain 1 pound sauerkraut. Cut about 14 ounces kielbasa sausage crosswise into 1/2-inch-thick rounds.

Step 2

Heat 1 tablespoon unsalted butter and 1 tablespoon vegetable oil in a large skillet over medium heat until the butter is melted and the oil is shimmering. Add the kielbasa in an even layer. Cook until browned on the bottom, about 3 minutes. Flip and cook until browned on the second side, about 3 minutes more. Transfer to a bowl or plate using tongs or a slotted spoon, leaving the fat in the skillet.

Step 3

Add the sauerkraut, red onion if using, 2 tablespoons packed light brown sugar, and 1 tablespoon spicy brown, whole-grain, or Dijon mustard if using to the skillet. Cook, stirring constantly, until the sauerkraut is heated through and onion is softened, 5 to 8 minutes. Taste and season with freshly ground black pepper as needed.

Step 4

Return the kielbasa to the skillet and toss to combine. Garnish with fresh thyme leaves or finely chopped parsley leaves if using.