In a bowl, combine all the ingredients. Refrigerate until ready to serve.
With your hands or a hamburger press, shape the meat into four patties. Season with salt and pepper.
In a non-stick skillet, cook the patties in the oil for 4 to 5 minutes on each side, or until they are cooked through (see note). Place a slice of cheese on each patty and continue cooking until the cheese starts to melt. Set the patties aside on a plate and keep warm.
In the cleaned skillet, toast the buns.
Spread the mayonnaise on the inside of the buns. Top with the patties, tomato slices and lettuce. Close the buns.
A hamburger press is a kitchen tool that makes uniformly sized and shaped patties.