Wash red leaf lettuce. Wrap in paper towel or a clean dish towel to dry.
Spread each slice of bread with 1 tsp of olive oil. You only need to oil one side. Toast in toaster oven or in the frying pan over medium heat. You are not toasting until crispy. You are just refreshing the bread and getting a slight crunch on the outside.
Once bread is toasted, put 4 slices, oiled side down, on a cutting board or plate. Spread the non-oiled side with 1 Tb mayo and 1 tsp honey for each slice.
Heat the frying pan to medium heat. Shape ground beef into 4 patties. Try to make them thin enough so that they almost are almost the size of the sandwich bread, but it won't be perfect. Season each side with salt and pepper.
Add 1 tsp cooking oil to pan. Fry the beef patties for 2-4 minutes on each side. The amount of time you cook them will depend on how well done you want them. If well done, the juices should be clear. If you prick the patty and red juice comes out, it is either rare or medium rare. The thinness of the patty will also vary the cooking time.
Once cooked, place each patty on the sliced bread with mayo and honey. Top with cheese. Let it sit and rest while you fry the eggs.
Clean out pan in order to fry the eggs. Heat over medium heat and add 1 tsp cooking oil. Crack eggs into pan. Fry one at a time if 4 eggs is too much to handle or the pan is not big enough. Cook until whites are no longer runny.
Slide one egg onto each hamburger patty. Top with red leaf lettuce and second slice of bread. Careful not to let the yolk run all over when you take a bite.
Dish count = cutting board, knife, spatula, frying pan