In a medium bowl, mix together the beef, salt, paprika, garlic powder, and ground pepper. Shape into four patties that are roughly the size and shape of the pieces of bread. (See photo in the post.)
1 pound ground beef, 1 1/2 teaspoons kosher salt, 3/4 teaspoon paprika, 1/4 teaspoon garlic powder, 1/4 teaspoon ground pepper
Melt the butter in a large skillet over medium heat. Add the onions, and sauté until onions are translucent, about 5 to 7 minutes. Remove the onions from the skillet with a slotted spoon. Set aside.
2 tablespoons unsalted butter, 1/2 small yellow onion
Add the patties to the skillet and cook until desired doneness, about 2 minutes on each side. Remove from the skillet and set aside.
Place four pieces of bread on a cutting board. Butter one side of each piece of bread, this is the side that will go face down in the skillet. Spread half a tablespoon of sauce, if using, on each piece. Then add a slice of Swiss cheese to each piece. Add the patties to each partial sandwich. Top with onions, add a piece of cheddar cheese. With the remaining four pieces of bread, add another half tablespoon of sauce, if using, to one side and butter to the other. Place it sauce side down on the in-progress sandwiches.
8 slices rye bread, 4 slices Swiss cheese, 4 slices cheddar cheese, 1/4 cup sauce
Place a clean skillet over medium-low heat. Add the sandwiches and cover the skillet. Cook the sandwiches for 2 minutes on each side.