In a bowl, blend the ground meat with the salt and pepper, mixing well but not over mixing. Divide into four 8-ounce portions and press flat with a burger press or between plates, should be 1/2-inch thick. Next, on a preheated flat top or griddle, sear the burgers on the first side, 4 minutes, and then flip and repeat the process. Cook the burgers until the internal temperature reaches 140 degrees F for medium.
For the buns, preheat a saute pan over medium heat (or use the griddle from the burgers). Then spread butter on both sides of the interior of the buns. Toast the buns until browned, 1 to 2 minutes.
Finally, heat the oil in a saute pan over high heat. Add the eggs and cook until the whites are set, with a soft yolk, for over-medium eggs.
To build, stack a burger on a toasted bun with 2 bacon slices, a tomato slice, a fried egg and the bun top. Repeat with the remaining ingredients.