Season the chicken breasts with salt and black pepper on both sides.
Set up a breading station with three shallow dishes: one with flour, one with beaten eggs, and one with a mixture of breadcrumbs and Parmesan cheese.
Dredge each chicken piece in flour, shaking off excess, then dip in beaten eggs, and finally coat with the breadcrumb mixture, pressing down to adhere.
Heat olive oil in a large skillet over medium-high heat.
Fry the chicken in batches until golden brown and cooked through, about 3-4 minutes per side. Add more oil as needed.
Transfer cooked chicken to a paper towel-lined plate to drain excess oil.
Serve Chicken Milanese hot with a side salad or lemon wedges, if desired.