Mix together sirloin, egg, pepper and salt in a large bowl.
Shape into 4 patties.
Cook patties in a large skillet over medium-high heat 4 to 5 minutes on each side or until browned. Remove patties, reserving drippings.
Sauté onion in drippings 2 minutes.
Add tomatoes and water.
Cook, stirring occasionally, 3 to 4 minutes.
Return patties to skillet; spoon tomato mixture over patties.
Cover and cook 15 minutes; uncover and cook 5 minutes.
Place 1 cheese slice on each patty.
Cover and cook 3 minutes.
Sprinkle with basil.
Serve over rice.