In a small to medium bowl add your anchovy and a little salt. Using the back of a spoon and the side of the bowl mash up the anchovy until it it is all broken up and looks more like a paste. Add the lemon juice, grated garlic clove, and pepper, whisk to combine. Whisk in the 4 tablespoons of oil starting slowly to form a dressing. Season with more salt and pepper if needed and reserve. Remove 1 tablespoon of dressing to a small bowl to put on the chicken.

Preheat the outdoor grill or indoor grill pan. Before you season your chicken, using a pastry brush, take some of the dressing from the larger bowl and brush it on the cut sides of the lettuce. Reserve for later. Do this before you do it to the chicken so you do not touch raw chicken before you touch the lettuce.

Now take your chicken and coat on both sides with the 1 tablespoon of reserved dressing using a pastry brush. Season with a little more salt and pepper and place on a preheated grill or indoor grill pan. Cook for about 4 minutes per side until no longer pink. Remove the chicken from the grill and let it rest for at least a minute before cutting into it.

Place your seasoned lettuce cut side down on the grill for one to two minutes to get a little char on it. Place the lettuce on a plate with a piece of chicken and more dressing. Take your wedge of cheese and shave off curls using a vegetable peeler or just toss some grated cheese over the top. Enjoy!