Preheat the grill to medium-high. In a large bowl, mix the ground beef, spinach, onion, Worcestershire sauce, and 3 teaspoons each of the salt and pepper.
Divide the meat equally into 12 portions and form into patties about 1 inch thick. Season both sides of the patties lightly with salt and pepper.
Lightly brush the grill grates with vegetable oil and place the patties on the grates. Grill the patties for 4 to 5 minutes, then flip and grill 4 minutes more for medium. Place a slice of cheese on top of the patties and cook an additional 1 minute or until melted. Toast the buns (if desired), cut sides down, 30 seconds to 1 minute, or until lightly toasted.