Denver Omlette Burger

My nephew recently went to Bulldogs Grill in Wauconda, Illinois. He came home raving about both the variety and awesomeness of their burgers. This recipe was inspired by a burger on Bulldogs' menu. I topped my first version with a traditional omlette. The second time around, I topped the burgers with the omlette stuffing and then topped that with two poached eggs. I'm including instructions for the first version, but feel free to adapt it by making all or half of the burgers with poached eggs. We had a variety of start times for tonight's dinner so I make one omlette (4 eggs) for two burgers. Later, I made the second version with poached eggs on top. Both got rave reviews. Enjoy!

Makes 4 omlette burgers and 2 plain (for the kids).

Ingredients
Burger
2 pounds ground beef
1 egg, slightly beaten
sea salt
freshly ground black pepper
Omelette
2 Tbsp grass-fed butter or coconut oil
8 eggs
4 green onions, sliced thin
4 oz mushrooms, sliced thin
1/2 cup ham, julienne sliced
1/2 cup green bell pepper, diced

Preparation

1. Combine burger ingredients in a large bowl and use your hands to thoroughly combine. Divide mixture into 6 patties. 
2. On a preheated grill, grill pan, or broiler, cook burgers until they reach your desired degree of doneness. Set aside and keep warm.
3. To make omlette, warm 1 Tbsp fat in a large skillet. Add onions, mushrooms, ham, and pepper. Saute for 4-5 minutes or until onion becomes clear and pepper and mushroom are cooked. Remove from pan and set aside.
4. Scramble eggs in a small bowl. Add more fat to skillet, if needed, then pour half of the eggs into the skillet. Swirl the skillet, if necessary, to make sure the egg is in an even layer. When eggs are almost cooked through, add half of ham mixture to one side of the egg and fold empty side of egg over the top. Cook for an additional 1-2 minutes or until cooked through. Season with salt and pepper, if desired. Remove from skillet and keep warm. Repeat process to make second omlette.
5. To serve, place one patty on each plate. Cut each omlette in half and place on top of burgers. Great served with spicy sweet potato fries.

Here is version 2 with poached eggs on top.