Combine ground beef, thyme and garlic in medium bowl, mixing lightly but thoroughly. Lightly shape into eight 1/2-inch thick patties. Brush both sides of onion slices with oil. Place patties and onion slices on grill over medium, ash-covered coals.
Grill patties, uncovered, 11 to 13 minutes to medium (160 degrees F) doneness until no longer pink in center and juices show no pink color, turning occasionally. Grill onions 15 to 20 minutes or until tender, turning occasionally and brushing with oil. Season patties with salt and pepper, as desired.
Add desired cheese to burgers about 1 minute before removing from grill. Place cheese-topped burgers on bottom of each bun and top with 1/2 of grilled onions. Close sandwiches. Cover and refrigerate remaining 4 burgers and onions.
Yield: 4 servings
Total preparation and cooking time: 35 to 45 minutes
* Any type of sliced cheese may also be used to top burgers, including Cheddar, Swiss, provolone and Gouda.
Recipe and photo credit: Cattlemen's Beef Board and National Cattlemen's Beef Association.