- 3 pounds lean ground beef
- 1 cup (packed) crumbled feta cheese
- 2 teaspoons dried oregano
- 1 1/2 teaspoons salt
- 1 1/2 teaspoons ground black pepper
- 8 large garlic cloves, peeled
- 1/2 cup plus 1 tablespoon extra-virgin olive oil
- Nonstick vegetable oil spray
- 2 medium red onions, peeled, each cut crosswise into 4 slices
- 8 hamburger buns
- 2 large tomatoes, each cut crosswise into 4 slices
- Break up beef in large bowl. Sprinkle feta, oregano, salt, and pepper over; toss. Divide into 8 portions; form each into 41/2-inch patty, pressing in center to form slight indentation. DO AHEAD Can be made 1 day ahead. Cover; chill.
- 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.
- Spray grill rack with nonstick spray. Prepare barbecue (medium-high heat). Brush onion with 1 tablespoon oil; sprinkle with salt and pepper. Place burgers and onions on grill. Cover; cook 5 minutes. Turn; cook until onions are charred in spots and burgers are medium-well, about 4 minutes longer.Transfer to plate. Brush cut sides of buns with garlic oil. Place buns, cut side down, on grill; toast about 1 minute. Turn; cook until heated, about 1 minute.
- Place burgers on bun bottoms. Top each with onion, tomato, and bun top.