Prepare the Chicken: Place the chicken breasts between two sheets of plastic wrap or parchment paper. Using a meat mallet or rolling pin, pound the chicken to an even thickness, about 1/4 inch.
Set Up the Dredging Station: In three separate shallow bowls, place the flour, beaten eggs, and a mixture of breadcrumbs and grated Parmesan cheese. Season each component with salt and pepper.
Dredge the Chicken: Lightly coat each chicken breast in flour, shaking off the excess. Dip the chicken into the beaten eggs, allowing any excess to drip off. Finally, coat the chicken in the breadcrumb and Parmesan mixture, pressing lightly to adhere.
Fry the Chicken: In a large skillet, heat olive oil over medium-high heat. Once the oil is hot, carefully add the chicken breasts. Fry for 3-4 minutes on each side, or until golden brown and cooked through. Avoid overcrowding the pan; cook in batches if necessary.
Serve: Transfer the cooked chicken to a paper towel-lined plate to drain any excess oil. Serve immediately with lemon wedges on the side.