Heat the oil in a large nonstick skillet over medium-high heat. Add the sausages and cook, turning occasionally, until browned all over, 6 to 8 minutes. Add a splash of water, cover, and cook until the sausages are just cooked through, about 2 minutes. Transfer to a plate to cool. Once cooled, slice into 2-inch pieces and reserve.
Reduce the heat under the skillet to medium and add the butter and caraway seeds, stirring until the butter is melted. Add the fennel and apple; cook, stirring, until slightly softened, about 3 minutes. Add the sauerkraut and sausage pieces and cook, stirring, until the sauerkraut is hot, about 3 minutes more. Season with salt and pepper. Garnish with fennel fronds.
Recipe courtesy of Valerie Bertinelli