Divide the ground chuck into 6 equal pieces, then divide each piece in half. Roll the 12 pieces into tight balls and press flat, until the patty is slightly larger than the bun. Make sure the meat is compacted, because if the meat is too loose the fillings will seep out and make a mess on the grill.
Cut each slice of cheese into square quarters and place the four quarters on a patty. Place another patty on top and press down around the edges, making a tight seal. Place the shaped patties on a platter and cover with some plastic wrap. Chill the burgers for about 30 minutes.
Preheat the grill. Place patties on the grill and cook over high heat for 6 minutes. Flip the burgers and pierce the cooked sides with a sharp knife to let a little steam escape from the molten cheese. Cook another 4 to 6 minutes (or longer) depending on your doneness preference, then remove from the grill. Let the burgers rest and cool a few minutes, then serve with your favorite toppings.