Combine ground beef with garlic powder, onion powder, salt, and pepper in a mixing bowl. Mix gently and form into three equal-sized patties.
Heat a skillet over medium heat and cook patties for about 4–5 minutes on each side. Add cheese slices on top during the last minute of cooking.
Spread butter on one side of each slice of bread. Assemble the melts with a patty and cheese between two slices of bread.
Grill each sandwich in a skillet over medium-low heat until golden brown and crispy, about 3–4 minutes per side.
Remove from heat, let cool for a minute, slice in half, and serve warm.