Preheat a grill or grill pan to medium high. Make the dressing: Chop 2 garlic cloves and puree with 1/2 cup olive oil, the anchovies and lemon juice in a blender until smooth; season with salt and pepper. Pound the chicken with a mallet or heavy skillet until about 1/8 inch thick. Season with salt and pepper and toss with 1 tablespoon of the Caesar dressing. Grill the chicken until golden and crisp, 3 to 4 minutes per side. Brush the bread with olive oil on both sides and grill, turning, until toasted, about 2 minutes. Rub with the remaining garlic clove. Brush the romaine with 1 to 2 tablespoons of the dressing and grill until marked, 1 to 2 minutes per side. Chop the lettuce and transfer to a bowl. Cut the bread and chicken into bite-size pieces and add to the bowl. Toss with the remaining dressing, the parmesan, and pepper to taste. Garnish with more parmesan.