Build a medium-hot fire in your grill or preheat a stovetop grill pan.
Cook the bacon in a sauté pan over medium-high heat, turning once until crisp, 5 minutes. Remove the bacon to paper towels to drain. Reserve the bacon fat in the pan.
Form the ground beef into 4 patties, each about 3 ½ inches in diameter. Season the patties with kosher salt and cracked black pepper. Place the burgers on the grill or in the grill pan and cook for 3 minutes. Flip and top each burger with a slice of cheese. Grill for 3 minutes for medium rare. Remove to a plate. Add the English muffins to the grill or grill pan and toast for 1 minute.
Cook the eggs sunny-side up in the bacon fat while the burger rests.