Sprinkle both sides of steak with thyme, salt, and pepper. Place steak on a broiler pan coated with cooking spray; arrange garlic cloves around steak. Broil steak and garlic 5 to 6 minutes on each side or until desired degree of doneness. Transfer steak to a cutting board; cover loosely with foil to keep warm.
Cut off bottom of each garlic clove. Squeeze out soft garlic into a food processor; process until smooth. Add broth; process until combined. Transfer garlic sauce to a microwave-safe dish. Microwave at HIGH 40 seconds.
Cut steak diagonally across grain into thin slices; spoon garlic sauce over steak. Garnish with fresh thyme, if desired.