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.
For the dressing: whisk together all ingredients. Season with salt and pepper to taste. Adjust any of the ingredients to taste. Toss the lettuce and tomatoes in the dressing.
Warm the rolls in a 350 degree oven for 3 to 5 minutes.
Place the chicken on the roll with lettuce mixture and top with shaved asiago.
Serve with chips and pickle.
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.