Shape the ground beef into four uniform portions, each weighing approximately ¼ pound. Flatten the patties to a diameter of at least 4 inches. Sprinkle both sides generously with salt and pepper.
Cook the patties using your preferred method—grilling, pan-searing, or broiling—until they reach your desired doneness.
Place a slice of American cheese on each patty just before removing them from heat, allowing it to melt over the surface.
In a small saucepan, stir together the chopped roasted green chiles, 1 teaspoon of salt, and 2 teaspoons of garlic powder. Warm the mixture over low to medium heat until heated through, adjusting seasoning if needed.
Assemble each burger on a bun with the cooked beef patty, a generous spoonful of warm green chile sauce, and any desired toppings such as onion, lettuce, tomato, and mustard.