In a medium bowl, combine ground beef, salt, and black pepper. Mix gently to combine without overworking the meat.
Divide the beef mixture into two equal portions and shape each into a thin patty slightly smaller than the bread slices.
Heat vegetable oil in a skillet over medium heat. Add diced onions and cook until softened and translucent, about 3 minutes. Remove onions and set aside.
In the same skillet, cook the beef patties for about 3-4 minutes per side or until cooked through and browned. Remove from skillet and set aside.
Spread softened butter evenly on one side of each bread slice.
Place two bread slices, buttered side down, on a clean skillet over medium heat.
On each bread slice, layer one slice of Swiss cheese, one cooked beef patty, half of the cooked onions, and another slice of Swiss cheese.
Top each with the remaining bread slices, buttered side up.
Grill the sandwiches for about 3-4 minutes per side, pressing down gently with a spatula, until the bread is golden brown and the cheese is melted.
Remove sandwiches from skillet, let cool for 1-2 minutes, then slice in half and serve immediately.