Combine all of the burger ingredients except for olive oil together in a large mixing bowl until well combined.
Form the burger mixture into 6 equal sized patties.
Heat olive oil over medium-high heat in a large, deep skillet. When oil is hot enough to sizzle, add patties carefully. Cook each side for approximately 5-7 minutes or until each burger reaches 160 degrees or your preferred level of doneness. Set burgers aside on a plate.
In the same pan, without washing out crispy bits and pan juices, melt the butter over medium-high heat. Add the mushrooms, onions, and garlic and sauté for 5-7 minutes. Add worcestershire, Italian seasoning and salt and pepper, cooking an additional 2-3 minutes.
Add flour and fully coat mushroom mixture to form a roux. Cook 2-3 minutes or until the roux is lightly toasted. Then gradually add broth 1/2 cup at a time, whisking frequently in between additions. Make sure you scrape the bottom of the pan to deglaze it and add more flavor. Once the gravy begins boiling, reduce heat to low.
Continue whisking until gravy is thickened and then add hamburger patties. Make sure the patties are fully submerged.
Simmer for five minutes on low to ensure everything is heated all the way through.
Serve each burger patty with gravy on top of a bed of rice. Top each with a fried egg.
Enjoy!