Melt the 1 Tbsp. butter in a skillet set over medium to medium-high heat. Add onions and apples and cook until tender, about 5 minutes. Cool to room temperature. Use the remaining butter to lightly coat one side of each bread slice. Set 4 of the slices, buttered-side down, on a work surface. Spread the top of those slices with mustard. Divide and top the mustard with half the cheese. Divide and top cheese with the meat, apple/onion mixture and sauerkraut.
Top the sauerkraut with remaining cheese.
Top sandwiches with remaining 4 bread slices, setting them buttered-side up.
Set a large non-stick skillet over medium-low heat. Set in the sandwiches and slowly grill 4 to 5 minutes per side, or until the cheese is melted. Cut each sandwich in two and serve.