In a large nonstick skillet, cook the bacon over moderate heat until crisp, about 6 minutes. Drain on paper towels. Pour off all but 1 tablespoon of the bacon fat in the skillet.
Preheat a grill pan. Shape the meat into four 5-inch patties and season generously with salt and pepper. Grill over moderately high heat until lightly charred, about 3 minutes. Flip the burgers and top with the smoked cheddar. Cook for about 3 minutes longer for medium-rare meat.
Meanwhile, in the reserved bacon fat in the skillet, fry the eggs over-easy over moderate heat, about 3 minutes. Set the burgers on the bottoms of the English muffins and top with the pickled onions, bacon and fried eggs. Serve with ketchup and mustard.