Make the croutons: Preheat the oven to 350 degrees F. Toss the bread cubes in a large bowl with 1 tablespoon olive oil.
Spread on a baking sheet and bake until crisp, tossing halfway through, about 20 minutes. Meanwhile, make the dressing: Puree the yogurt, 2 tablespoons parmesan, the garlic, anchovies, lemon juice, mustard and 2 tablespoons water in a mini food processor or a blender. Pound the chicken between 2 pieces of plastic wrap with a heavy skillet until 1/2 inch thick.
Brush a rimmed baking sheet with the remaining 1 tablespoon olive oil; add the chicken and season with salt.
Brush evenly with 1 tablespoon of the dressing and sprinkle with 2 tablespoons parmesan. Broil, undisturbed, until golden and cooked through, about 5 minutes.
Transfer to a cutting board. Toss the lettuce, croutons and the remaining dressing and 3/4 cup parmesan in a large bowl. Thinly slice the chicken. Divide the salad among bowls, top with the chicken and season with pepper.