Make the Gary Sauce: In a small bowl, stir together the mayonnaise, ketchup, Dijon mustard, sweet pickle relish, smoked paprika, garlic powder, and black pepper until smooth.
Make the slaw: In a medium bowl, combine the sauerkraut and your slaw base of choice. Use chopped cooked collards, chopped cabbage, or a mix of both. If using all three, aim for roughly equal parts sauerkraut, collards, and cabbage. Add 2 to 3 tablespoons Gary Sauce and mix until evenly coated. Add more sauce if needed. The slaw should be dressed, not dry.
Grill the bread and melt the cheese: Heat a large skillet or griddle over medium heat. Butter one side of each slice of bread. Place the bread butter-side down in the skillet. After a minute or two, flip each slice and immediately add Swiss to half the slices and provolone to the other half. Let the cheese melt while the second side lightly toasts, then transfer the bread to a plate or sheet pan.
Crisp the corned beef: In the same skillet, add 1 to 2 tablespoons butter and increase the heat to medium-high. Add the leftover corned beef in an even layer. Let it cook long enough to brown, then stir and continue cooking until the edges are crisp and caramelized.
Build the sandwiches: Spread Gary Sauce on both cheese sides of the bread. Pile the crispy corned beef onto one slice, then top with a generous amount of slaw. Add another swipe or drizzle of sauce if desired. Close with the second slice of bread. Secure each sandwich with 1 to 2 toothpicks before slicing, if needed.
Serve: Slice in half and serve hot.