Preheat oven to 375F.
Combine meat with salt, pepper, Worcestershire and finely chopped bacon. Form into 4 patties that are thinner at the center than the edges for even cooking.
Arrange remaining 8 slices of bacon on a slotted broiler pan and bake to crisp, 15 minutes or so.
Grate potatoes on the large side of box grater and season with salt. Drain in a strainer for 10-15 minutes. Press out the excess liquid and combine potatoes with grated onion, pepper, egg and just enough flour to bind the potatoes, 2-3 tablespoons. Heat a thin layer of oil in a large skillet over medium to medium-high heat. Add potatoes in 4 thin pancakes, 4 inches round. Saute hash brown cakes until deeply golden on each side, about 7-8 minutes, turning once. Remove to cooling rack set into rimmed baking sheet.
Heat griddle or cast-iron skillet to medium-high.
Remove bacon from oven and toast rolls while potatoes cook. Turn oven off; add potato cakes to a baking sheet to keep warm in oven. Reserve buttered rolls and bacon.
Cook burgers on hot griddle or in the skillet about 10 minutes, turning once. Top with cheese to melt in last 1-2 minutes of cook time.
While cheese melts, melt 1 tablespoon butter over medium heat in the skillet you made the hash brown cakes in. Fry 4 eggs (over medium to hard), season with salt and pepper.
Place cheeseburgers on bun bottoms and top with 2 slices of bacon crossed, fried egg, a potato cake, lots of ketchup and a bun top.
Makes 4 burgers. Serve with Bloody Mary or Bloody Bull (splash of beef stock) cocktails, celery sticks.