Mix the yogurt, thyme, ground beef, salt and pepper. Then, create 8 patties from the meat mixture.
Cut the cheese into slices. Put one slice of cheese in between two patties, and then seal the edges. Do the same with the rest of the meat and cheese.
Prepare the grill by brushing the grate with oil, and place the meat patties onto the hot grate. Cook covered for 20 minutes, making sure the meat is cooked all the way through and the cheese is completely melted.