Stack the four slices of cheese and cut into 4 even squares. Set aside
In a medium bowl, season beef with garlic powder, onion powder, salt, and pepper. Gently mix with your hands until combined.
Divide the meat into 8 equal portions and form them into balls. Form one juicy lucy at a time: press two of the meat balls into even, thin 1/4 inch patties. Top one patty with four of the small cheese squares in the center, leaving about an 1/2 inch boarder. Place the other patty on top, and gently press the edges to seal the cheese in. Cup the stuffed patty to round out the edges. Repeat 3 more times.
Heat a large cast iron skillet over medium heat until hot, about 3 minutes. Place burgers onto pan (as many will fit without being crowded). Cook undisturbed until dark golden-brown on the bottom, about 4 minutes. Using a spatula, flip the patties and cook until the second side is dark golden-brown and the patties are cooked through, about 4 minutes.
Assemble burger. Place a burger on a toasted bun (if desired) and top with desired toppings.