Preheat your grill to medium heat, roughly 350F. (You should be able to hold your hand just above the cooking grate for 5-7 seconds.)
While the grill preheats, make your patties. Place the beef, Worcestershire sauce, minced garlic, salt, and pepper in a medium bowl. Mix until just combined, being careful not to over-work the meat. (Over-worked meat means tough burgers.)
Divide the ground beef into 12, roughly equal, pieces. Roll each piece into a ball. Flatten two of the balls as thin as possible (roughly ¼ inch) on two pieces of plastic wrap or butcher paper. Arrange roughly ¾ oz of cheese over the center of one of the patties, leaving at least a ½ inch rim of bare meat around the cheese. Flip the other patty over top of the cheese and gently pull the paper off of the top. Firmly press the edges of the patties to seal in the cheese, making sure there are no holes. Continue with the remaining meat until you have 6 stuffed burger patties.
Flip the burgers onto the hot grill grates. Cover the grill (with your bottom vents completely open and your top vents half open). After 2-3 minutes flip the burgers and cook for an additional 2-3 minutes on the second side.
Place the burgers onto the split buns and add your desired toppings. Be sure to let the burgers rest for 3-5 minutes before biting into them.