In a medium bowl mix together the Egg, Italian Dressing, Worcestershire Sauce, Rosemary, Garlic, and Ground Pepper completely mix and set aside.
Place your beef in a large bowl, pour the egg wash over and your chopped onion and mix thoroughly. Place the meat mix in the refrigerator for an hour to allow your flavors to really soak into it.
In a heated skillet melt your butter and add your sliced onion and pepper to taste, you want to stir it frequently so your onions don't burn. Once the onions have caramelized and pour in your beef gravy, allow to the onions to absorb the gravy. (7-10 minutes)
Form your patties and it's time to cook your burgers...