Prepare the dressing by stirring the lemon juice, garlic, and anchovy paste until smooth in a small bowl. Add the remaining dressing ingredients and stir well. Cover and refrigerate for a minimum of 1 hour.
Prepare the rub by mixing the oregano, thyme, lemon pepper, garlic powder, onion powder, brown sugar, and salt in a small bowl.
Rinse the chicken and pat it dry with paper towels. Use your fingers to rub both sides of each piece of chicken with the Herb Rub. If you have time, set aside for 15-30 minutes. For intense flavor, cover and refrigerate for up to 24 hours.
Spray a broiler pan with nonstick cooking spray. Arrange the chicken on the pan and spray the tops with a light coat of cooking spray. Broil 6 inches under a preheated broiler for 12-15 minutes, turning occasionally, until the meat is browned.
Remove the chicken to a cutting board to cool for 5 minutes. Slice thinly across the grain and set aside.
Put the lettuce in a large bowl. Add the dressing and toss to mix. Add the Parmesan cheese and toss.
Arrange a quarter of the lettuce mixture on each of 4 plates. Sprinkle the croutons over the lettuce on each plate and arrange a sliced chicken breast over each salad.