Use a sharp knife to slice the kielbasa into approximately 1/2-inch slices.
Add olive oil to a large 12-inch skillet. Arrange kielbasa rounds in the skillet in a single layer. Cook for 2-3 minutes per side or until browned. Remove from the skillet to a platter, leaving fat in the skillet.
To the skillet add the red onion and garlic. Cook for 1-2 minutes over medium high heat. Add the sauerkraut stirring to combine.
Next, add light brown sugar, mustard and black pepper to the sauerkraut mixture. Cook over medium-high heat until the sauerkraut is heated through and onion has softened, around 5 to 8 minutes.
Return the kielbasa slices to the skillet and stir to combine. Simmer for 3-5 minutes.
Serve immediately garnished with fresh parsley or thyme.
Notes
Protein: You can use smoked sausage, pork sausage, turkey kielbasa or chicken sausage in place of kielbasa.
Mustard: You can use Dijon mustard or creole mustard in place of horseradish mustard or whole grain mustard. The amount would remain the same.
Seasonings: You can add a 1/2 teaspoon of fennel seeds or caraway seeds to the onions.
Salt: The sauerkraut will likely have ample salt already added to the flavor. Taste and adjust the salt, adding more to your personal taste.
Potatoes: You could add cubed potatoes to the onion and garlic, cooking until they're fork tender before proceeding with the recipe.
Apples: You could also add diced Granny Smith apples to the pot for a hint of sweetness.