In a large bowl, mix together ground beef, yogurt, thyme, and salt and pepper. Form meat into 8 patties, about 2 to 3 inches in diameter.
Cut the cheese into 4 slices. Place one cheese slice between two patties, and seal the edges. Repeat with remaining beef patties and cheese slices. Set bifteki aside.
Brush grate with oil, and arrange bifteki on hot grate. Cover, and cook for 15 to 20 minutes, or until meat is cooked through and cheese is melted.
