Season the chicken with 1 tablespoon olive oil, a good pinch of salt and pepper, garlic powder, onion powder, and cayenne pepper. Preheat a stove-top grill pan over high heat. Once hot, place the chicken on and grill for about 6 minutes per side or until the internal temperature reaches 165°F. Transfer to a cutting board and allow to rest for about 10 minutes before slicing into thin slices; set aside.
Preheat the broiler to high. Place the bread slices on a baking sheet, in a single layer, and drizzle with the remaining olive oil. Place under the broiler and cook until the bread is golden brown and crispy on both sides, about 30 seconds to a minute. Keep a close eye so that it doesn't burn. Remove from the oven and once cool enough to handle, rub the toast slices with the whole garlic and season with a pinch of salt and pepper. Set aside.
To make the dressing, combine the egg yolk, garlic, lemon juice, 1 or 2 anchovy fillets (depending on how you like them), a pinch of salt and pepper, Parmesan, and Worcestershire sauce in a small food processor. Blend until just beginning to come together. Then while the machine is running, drizzle in as much of the oil as needed to create a smooth thickened dressing. Transfer to a bowl and stir in the mayo, if using. Give it a taste and adjust seasoning if necessary, adding more salt or pepper if needed.
In a large salad bowl, toss together the lettuce, a few tablespoons of the dressing (depending on how dressed you like your salad, and the Parmesan cheese until evenly combined.
To assemble, top the bread slices with the sliced chicken and the dressed salad. Shave Parmesan on top for garnish, if desired, and sprinkle with a bit of black pepper. Serve immediately and enjoy!