In small bowl whisk together mayonnaise, ketchup, grated onion, pickle relish, and paprika.
Place 2 tablespoons butter in nonstick skillet over medium high heat. Add onions and cook until golden brown approximately 10-15 minutes; stirring every few minutes.
Mix ground beef, Worcestershire Sauce, salt and pepper. Form into four equal patties. Preheat skillet and cook over medium heat until golden brown and cooked through; flipping halfway through the cooking process.
Spread a little more than 1 tablespoon of dressing on each slice of bread. Place a piece of Swiss Cheese on each slice of bread. Add browned onions and one beef patty to four of the slices. Top with the remaining slices to form four sandwiches.
Butter top side of bread and place butter side down in skillet over medium low heat and cook until golden brown. Butter other side of bread before flipping. Flip and brown other side until golden brown and cheese is melted. It is helpful to cover the skillet with aluminum foil while it is browning.