12 garlic cloves, peeled, divided
1 1/2 cups (packed) fresh Italian parsley sprig tops
1/3 cup white balsamic vinegar
1/4 cup (packed) fresh mint leaves
1/4 cup (packed) fresh basil leaves
1 teaspoon dried oregano
1/4 teaspoon dried crushed red pepper
1 cup olive oil
8 large boneless chicken breast halves with skin
Nonstick vegetable oil spray
8 bricks, each wrapped in foil
Cook 8 garlic cloves in boiling water 2 minutes. Drain garlic. Place in processor and cool. Add remaining 4 garlic cloves and next 6 ingredients. With machine running, gradually add oil, blending until thick sauce forms. Season with salt. Do ahead Can be made 2 days ahead. Transfer to bowl; cover and chill.
Place chicken in large resealable plastic bag. Add 1/2 cup sauce and turn to coat evenly. Chill at least 1/2 hour and up to 4 hours, turning bag occasionally.
Spray grill rack with nonstick spray and prepare barbecue (medium-high heat). Place chicken, skin side down, on grill. Top each piece with 1 foil-wrapped brick. Grill until skin is golden brown and crisp, about 5 minutes. Remove bricks. Turn chicken over; grill until cooked through, about 5 minutes. Arrange chicken on platter. Spoon some sauce over. Serve, passing remaining sauce separately.