Begin by placing the chicken breasts between two pieces of plastic wrap. Using a meat mallet or rolling pin, gently pound the chicken until it's about ½ inch thick.
In a large mixing bowl, whisk together the eggs, sea salt, and freshly-cracked black pepper. In a separate shallow dish, combine the panko breadcrumbs, finely grated Parmigiano Reggiano cheese, minced parsley, and grated garlic.
Dip each piece of flattened chicken into the egg mixture, allowing any excess to drip off. Next, dredge the chicken in the breadcrumb mixture, pressing gently to ensure it adheres well.
In a large skillet, heat the extra-virgin olive oil over medium heat. You want enough oil to cover the bottom of the pan.
Once the oil is hot, carefully add the breaded chicken cutlets to the skillet. Cook for about 4-5 minutes on each side, or until they turn golden brown and crispy.
Once cooked, transfer the cutlets to a paper towel-lined plate to drain any excess oil. Serve immediately with lemon wedges on the side.