Whisk together the eggs, parsley, Worcestershire sauce, ketchup, garlic powder, onion powder, salt, and pepper in a large bowl until well blended. Add the rice and stir to blend. Add beef and combine with rice mixture until just blended. Do not overmix. Shape into 24 (4-inch diameter) patties. Gently press back of spoon in center of each patty to indent slightly.
Heat a grill over high heat. Cook patties 4 minutes, turn patties and cook 2 minutes, top each with a cheese slice and cook 2 minutes or until internal temperature is 160 degrees F.