Preheat grill or grill pan to medium-high heat (about 375˚F).
In a large mixing bowl combine ground beef, water, salt, and pepper and mix until thoroughly combined.
Divide the mixture into 4 equal balls and divide and form each ball into two patties.
Place two pieces of cheese into the center of 4 of the 8 patties. Top each of the patties with cheese, with the remaining patties and pinch the ends together to seal completely.
Season the 4 stuffed patties with salt and pepper.
Brush oil onto the grill or grill pan and add the burger patties. Cook the patties for 5 to 6 minutes on each side for medium doneness. Remove from grill/grill pan and allow patties to rest for 4 to 5 minutes.
Brush burger buns with mayonnaise, ketchup and mustard. Top each bottom bun with a burger patty and finish with whatever toppings you desire. Serve.