While burgers are cooking you will want to 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. Reduce the heat to low and season the eggs with salt and pepper. Cover the pan and cook until the whites are set and the yolks are just beginning to firm around the edge, about 5 minutes.