Heat a gas grill to high heat. Grill the first side for 3 minutes or until golden brown and slightly charred. Flip over burgers. Cook 6 minutes or until it reaches desired doneness. When you have one minute left of grilling time place a slice of cheese on top of burger and let it melt.
While burgers are cooking, fry your eggs either on a skillet on the stove or on the grill. Heat a pan with 2 Tbsp butter over medium high heat. When the butter foams, break the eggs into the pan, spacing them about 2 inches apart.
When making your own burgers, use beef that is no leaner than 85%. Due to the high fat content, your burger will be juicy and full of flavor. Beware that higher fat meat will shrink more when they are grilled.