Mini Egg Burgers

Preheat a skillet over medium heat. Divide the ground beef into 4 equal portions and shape into small patties, about 2 inches in diameter. Season both sides with salt and pepper.
Cook the patties in the skillet for 2-3 minutes per side, or until browned and cooked through. Remove from the skillet and set aside.
In the same skillet, melt the butter. Crack the eggs into the skillet one at a time and cook sunny-side up for 2-3 minutes, or until the whites are set and the yolks are still runny.
Lightly toast the slider buns in a toaster or on a skillet until golden brown, about 1 minute.
Assemble the burgers by spreading 1/2 tablespoon of mayonnaise on the bottom half of each bun. Layer with shredded lettuce, a beef patty, a cooked egg, and a sprinkle of shredded cheddar cheese. Top with the other half of the bun and serve immediately.