Instructions

  1. Break up beef in large bowl.
  2. Sprinkle feta, oregano, salt, and pepper over (meat); toss.
  3. Divide into 8 portions; form each into 4 1/2-inch burgers, pressing in center to form slight indentation. *DO AHEAD Can be made 1 day ahead. Cover; chill.
  4. Puree garlic in processor; With machine running, gradually add 1/2 cup oil; process 30 seconds. *DO AHEAD Can be made 1 day ahead. Cover; chill.
  5. Spray grill rack with nonstick spray.
  6. Prepare barbecue (medium-high heat).
  7. Brush onion with 1 tablespoon oil; sprinkle with salt and pepper.
  8. Place burgers and onions on grill. Cover; cook 5 minutes.
  9. Turn onions and burgers; cook until onions are charred in spots and burgers are medium-well, about 4 minutes longer.
  10. Transfer to plate. Brush cut sides of buns with garlic oil and place buns, cut side down, on grill; toast about 1 minute.
  11. Turn buns; cook until heated, about 1 minute.
  12. Place burgers on bun bottoms and top each with onion, tomato, and bun top.