Preheat grill or grill pan on medium heat. Season both sides of the chicken with salt and pepper and drizzle with olive oil. Cook the chicken on each side until an internal temperature of 160 degrees is achieved. Let sit for 3 minutes before slicing.
Drizzle the bread with a little olive oil, season with salt, pepper, and oregano.
For the dressing: whisk together olive oil, garlic, dijon, Worcestershire, lemon juice, parmesan, and anchovy paste (if using). Season with salt and pepper to taste. Adjust the ingredients to taste.
Serve the chicken over the lettuce and drizzle with about 2 teaspoons of the dressing on top or more if desired (do not over dress the salad). Serve with bread. Garnish with parmesan.
Notes
Pro tips: Butterfly the chicken: Lay the breasts down on a cutting board, using a sharp knife parallel to the cutting board slice the breasts evenly through the middle (carefully) all the way in half.