Place chicken breasts between two sheets of plastic wrap or in a zip-top bag. Gently pound with a meat mallet or rolling pin until evenly flattened to about 1/2 inch thick. Season both sides with salt and pepper.
In one shallow bowl, place the flour. In a second bowl, beat the eggs. In a third bowl, combine the breadcrumbs and grated Parmesan cheese.
Dredge each chicken breast in the flour, shaking off excess. Dip into the beaten eggs, ensuring the chicken is fully coated. Finally, press into the breadcrumb mixture, coating both sides evenly.
In a large frying pan, heat the olive oil over medium heat. Once hot (about 350°F), carefully place the breaded chicken in the pan, ensuring not to overcrowd.
Fry the chicken for about 4-5 minutes per side, or until golden brown and cooked through. The internal temperature should reach 165°F.
Once cooked, transfer the chicken to a plate lined with paper towels to absorb excess oil. Serve immediately with lemon wedges and a sprinkle of chopped parsley if desired.
For a lighter version, you can bake the breaded chicken in a preheated oven at 375°F for about 20 minutes, flipping halfway through.
Consider marinating the chicken in some olive oil, garlic, and herbs for an hour before breading for added flavor.