Mix together the flour and salt and sprinkle on a plate. Dredge the chicken breast cutlets in the flour so they are completely coated.
Dip coated chicken in the eggs and allow any excess to drip off, then dip them into the breadcrumbs, being sure to press them down to ensure the breadcrumbs stick and form a thick coating.
Heat a heavy skillet, such as a cast iron pan, over medium heat. Coat the bottom with a thin layer of oil and heat. When the oil is hot, add chicken cutlets and fry for about 3-4 minutes on each side, or until golden brown and cooked through. Remove the cutlets from the pan when finished and place on a paper towel lined plate to cool. Once cooled, slice into thin strips.
Preheat oven to 400°F and line 2 baking sheets with parchment paper or prepare a pizza stone according to stone's directions.
Divide the pizza dough into 4 sections. Roll out one section on a floured surface to be about ¼” thick circle. Line half of the circle with fresh mozzarella slices and 1-2 Tbsp. parmesan, leaving the outer 1” empty.
Top the mozzarella with sliced chicken cutlets, basil leaves and additional mozzarella and parmesan. You should be left with about ¼ cup parmesan to top the calzones with. Fold the empty dough over the cheese and chicken to create a half circle and pinch the edges together well with floured fingers. Roll the edges inward to create a good seal.
Place the calzones onto the prepared pans. With a sharp knife, make 2-3 slits along the top to allow air out and brush the tops with olive oil and sprinkle with remaining parmesan cheese.
Bake for 15-20 minutes, until calzones have browned and you can see the interior bubbling. Remove from oven and allow to cool on pan slightly.