Heat the oven to 400°F. Put a rack in the middle position and choose a 10-inch oven-safe skillet.

Drain the sauerkraut in a colander. Press it with your hands or the back of a spoon to remove extra liquid so the skillet does not get watery.

Slice the kielbasa into 1/2-inch half-moons if it is not already cut. Thinly slice the onion and the apple.

Set the skillet over medium-high heat and add the olive oil.

Add the kielbasa to the hot skillet in one layer. Cook for 3 to 4 minutes, stirring once or twice, until the cut sides brown.

Transfer the kielbasa from the skillet to a plate. Leave the browned bits in the skillet because they will flavor the rest of the dish.

Lower the heat to medium and add the butter to the skillet.

Add the sliced onion to the melted butter. Cook for 3 minutes, stirring often, until it starts to soften.

Add the sliced apple to the skillet. Cook for 2 to 3 minutes, stirring, until the slices lose their raw look and start to bend.

Stir the Dijon mustard and black pepper into the onion and apple so they coat evenly.

Add the drained sauerkraut to the skillet. Cook for 2 minutes, stirring, until it is hot and any extra moisture has cooked off.

Return the kielbasa to the skillet and stir it through the sauerkraut mixture. Spread everything into an even layer.