Slice the chicken breast in half the thin way by placing your palm on the chicken and running your knife parallel to the cutting board through the center. This will create two thinner chicken cutlets.
Put plastic wrap or parchment over and under the chicken and use a kitchen mallet or anything heavy to pound the chicken thinner. It will also get larger and winder during this process. Repeat with the second piece.
Cut the chicken into 12 pieces that will be a good size for your buns.
Put the flour, eggs, and breadcrumbs each into their own shallow bowl. Add the parm to the breadcrumbs and season all 3 bowls with salt and pepper.
Bread the chicken pieces starting with a dredging in the flour, then a dip in the eggs, and finally the breadcrumb cheese mixture.
Bring about an inch of olive oil to medium high heat in a frying pan. Also preheat the oven to 350.
Cook the chicken about 3-5 minutes on each side to golden brown and cook through. Transfer to a rack to cool.
Top the chicken pieces with a spoonful of sauce, then some cheese. Bake for about 8 minutes to melt the cheese.
Build the sandwiches with a bottom pasta bun, then some sauce, then the chicken piece, then the top bun. Serve.