Form your burger patty and pack it nice and tight. Season both sides of the patty. You want to cut a whole in the center of the patty using a cookie cutter or small glass.
Cook the patty until browned on both sides and almost cooked all the way through.
While burger is cooking take 2 Tbsp. of of shredded cheese roughly in the shape of your bun add the bun on top and grill on medium/low until the cheese is crispy and golden (too much cheese and you will have more sticking to the pan then you will to the bun. Do this for both top and bottom bun
Back to the burger, pour your egg into the hole you had made in step #1. You might get a little over flow form the egg depending on how thick you made the patty. Cook on medium/low covered, until the egg is cooked how you like.
Put burger together and enjoy!!
Notes
Seriously hung over or not this is a great brunch. My son loves this burger (minus the hot sauce). He and I both like our eggs sunny side up so they tend to be a bit messy but completely worth it!Adapted from Average Guy Gourmet