Form beef into 3 equal-size patties. Using a small glass, cut out center of each patty to create a donut shape; combine excess meat to form a fourth patty and cut out center. Season patties generously with salt and pepper. In a large skillet over medium-high heat, melt butter. Add patties and cook 2 minutes, then flip. Crack an egg into center of each, season with salt and pepper, cover, and cook until egg whites are set, about 5 minutes more. Top with cheddar cheese and cover with lid to let melt, 1 minute. In a small bowl, stir together mayonnaise and Sriracha. Spread on toasted buns. Serve burgers on toasted buns with cooked bacon and lettuce.