Set a large 12-inch skillet with a lid over medium heat so it is ready when the potatoes come out of the microwave.

Put the halved potatoes into a large microwave-safe bowl with 2 tablespoons of water. Cover the bowl loosely with a plate or microwave-safe lid.

Microwave the potatoes for 5 to 6 minutes, until they are starting to soften but are not fully tender yet. A knife should go in with some resistance.

Add 1 tablespoon of the olive oil to the skillet. When the oil looks loose and shiny, add the sausage rounds in a single layer.

Cook the sausage for 2 to 3 minutes on the first side, then turn the pieces and cook 2 minutes more, until both sides have browned spots. Transfer the sausage to a plate.

Add the remaining 1 tablespoon olive oil to the same skillet. Add the sliced onion and cook for 4 minutes, stirring a few times, until it softens and starts to brown at the edges.

Add the sliced garlic and caraway seeds to the skillet. Stir for about 30 seconds, just until the garlic smells fragrant.

Drain any water left in the bowl of potatoes. Add the potatoes to the skillet, placing as many cut side down as you can.

Cook the potatoes for 4 to 5 minutes, stirring only once or twice, until the cut sides pick up golden brown color.

Sprinkle the black pepper over the potatoes and onions. Add the sauerkraut to the skillet and spread it around the potatoes instead of piling it all in one spot.

Pour the chicken broth into the skillet. Use a wooden spoon to loosen any browned bits stuck on the bottom of the pan.

Return the browned sausage and any juices from the plate to the skillet. Tuck the sausage pieces into the potatoes and sauerkraut.