**Cook the Sausage:** Heat the olive oil or butter in a large skillet or Dutch oven over medium heat. Add the sliced sausage and cook until browned on both sides, about 5 minutes. Remove from the skillet and set aside.

**Sauté Onions and Garlic:** In the same skillet, add the sliced onions and sauté until softened, about 3-4 minutes. Add the minced garlic and cook for an additional minute.

**Add Potatoes:** Add the cubed potatoes to the skillet and cook for 5-7 minutes, stirring occasionally, until lightly browned.

**Combine Ingredients:** Return the sausage to the skillet and stir in the sauerkraut, chicken broth, smoked paprika, and caraway seeds (if using). Season with salt and black pepper to taste.

**Simmer:** Cover the skillet and reduce the heat to low. Simmer for 20-25 minutes, or until the potatoes are tender and the flavors have melded together. Stir occasionally and add more broth if needed to prevent sticking.

**Garnish and Serve:** Remove from heat, sprinkle with fresh parsley if desired, and serve warm.