1. Cook the sausages in a 10-inch skillet according to package directions. Meanwhile, toast the bread, spread it with the butter, then the mustard, and set aside. Preheat the broiler.
2. Using the coarsest side of a four-sided grater, shred the apple into a small bowl, add the sauerkraut, and mix. Place 1/4 of the mixture on each slice of toast.
3. Split each sausage link in half lengthwise and place 3 split sausages on each sandwich. Top with the cheese, and broil 4 inches from the heat; for 4 minutes, or until the cheese melts.