1. Preheat grill to high.
2. Coat bread slices with cooking spray. Place the bread on grill rack coated with cooking spray; grill for 1 minute or until golden, turning once. Remove bread from grill. Cut 1 garlic clove in half; rub both sides of bread with cut sides of garlic clove. Discard clove.
3. Pat anchovy fillets dry with a paper towel. Combine remaining 2 garlic cloves, 2 anchovy fillets, juice, mustard, pepper, salt, and egg yolk in a blender; process until smooth. With blender on, add oil, 1 tablespoon at a time; process until smooth.
4. Place lettuce, cut sides down, on a grill rack coated with cooking spray; grill 2 minutes. Turn; grill 1 minute. Remove from heat; coarsely chop lettuce. Place lettuce in a large bowl; drizzle with dressing, tossing gently to coat.
5. Cut remaining 5 anchovy fillets in half lengthwise. Arrange about 3/4 cup salad on each of 10 plates; top each serving with 1 bread slice and 1 anchovy half. Sprinkle each serving with about 1 1/2 teaspoons Parmigiano-Reggiano.