Preheat oven to 375 F. Place a wire rack over a baking sheet; set aside. Season meat with salt & pepper. Divide into 4 equal portions; roll each into a ball & then flatten into patties.
Peel onion, cut off ends & slice into thick pieces. Place a large onion ring in the center of 2 patties.
Cut the cheddar cheese so that it is the same height as the onion rings & place the cheese pieces around the inner wall of the onion rings.
Put a smaller onion ring in the middle. Place a cooked slice of bacon inside the smaller onion rings, followed by an even smaller onion ring, followed by a cube of mozzarella cheese.
Cover the layered onion rings with 2 bacon strips each & wrap the ends under the onion rings.
Place the remaining 2 burger patties on top of each of the bacon wrapped onion rings. Seal the top & bottom layers of beef so that the center is fully covered.
Place flour on a plate & roll stuffed burgers in it to coat. Whisk egg & dip the floured burgers into the egg mixture.
Slightly crush french fried onions & dredge burgers in them. Place stuffed burgers on wire rack on baking sheet. Bake for 30 minutes.
Recipe Notes
If you prefer, instead of making 2 large stuffed burgers, divide the meat into 8 portions & make 4 smaller ones.