Start by pounding the chicken breasts to an even thickness of about 1/4 inch. This will help them cook evenly and make them tender.
Using a pastry brush, brush mustard over the chicken slices on both sides. Season each slice of chicken with salt and pepper.
In a shallow dish, add flour and season with salt and pepper. In a second shallow dish, whisk the eggs and season with salt and pepper. In the third shallow dish, combine Italian bread crumbs and Parmesan cheese.
Dip each chicken breast into the flour mixture, coating it thoroughly on both sides. Shake off any excess flour. Next, dip the coated chicken breast into the egg mixture, making sure it's fully coated. Allow any excess egg mixture to drip off. Finally, coat chicken breast with bread crumbs. Press the bread crumbs to ensure they stick to the chicken.
Heat about 1/4 inch of vegetable oil in a large skillet over medium heat. You can test if the oil is hot enough by dropping a small piece of bread into it. If it sizzles and turns golden brown within a few seconds, the oil is ready.
Carefully place the coated chicken breasts into the hot oil, 1-3 at a time, depending on the size of your skillet. Cook for about 4-5 minutes per side, or until golden brown and cooked through. You may need to adjust the heat to ensure they don't burn.
Once cooked, transfer the chicken cutlets to a paper towel-lined plate to drain any excess oil. Repeat the frying process with the remaining chicken breasts, adding more oil if needed.
Serve the chicken cutlets hot, either on their own or as part of a delicious meal. They pair well with mashed potatoes, steamed vegetables, or a fresh salad.