Cut the chicken breast in half horizontally, so that you have 4 pieces of chicken. Place them in a Ziplock bag and proceed to pound the chicken breast so that you have 4 thin pieces of chicken. Season with salt and pepper and grill on both sides until completely cooked through. My grill took about 7 minutes.
While chicken is grilling make the aioli. Place the egg, crushed garlic cloves, and parsley into a blender. Blend until mixed and there are no garlic chunks, add the olive oil and salt and pepper to taste, a sprinkle of lemon juice may also be added. Blend until thickened. Set aside.
Heat medium skillet over medium-high heat. Melt 2 teaspoons of butter.
Generously butter 8 slices of bread on only one side. Sprinkle 1-1/2 tablespoons plus 1 teaspoon of parmesan on buttered side of bread. Push down to stick the cheese to the butter.
Reduce heat to medium-low. Place 2 slices of bread in skillet, cheese side down. Spread aioli on bread, then top with chicken, pancetta, 1/4 cup of mozzarella, and a pinch of parmesan and lemon zest. Place other slice of bread on top, butter side up.
Once it is golden brown, after a few minutes, flip over sandwich and bake until cheese in the sandwich is melted and the bread is a golden brown. Remove from heat and repeat process with remaining sandwiches.
Cut sandwiches in half and serve with a green salad. If you have extra aioli, have it on the side for those who want more.