Pound the chicken between 2 pieces of plastic wrap or parchment paper to ⅛” inch thick. Use a meat mallet, a rolling pin, or the back of a pan to flatten the chicken breasts.
To a bowl add flour, to a second bowl add eggs with vegetable oil and lightly beat until frothy. To a third bowl, add breadcrumbs.
Season chicken with salt and pepper, and heat ⅛ inch of oil in a pan. As you heat the oil dip each chicken cutlet in the flour shaking off any excess, then dip in egg (shake off excess), and finally in the breadcrumbs (do not press at all, just get coverage).
When the oil is hot and shimmering (add a few breadcrumbs to check), add chicken cutlets away from you (do not overcrowd the pan, and work in batches), and cook for 3 minutes moving the pan around so the hot oil evenly touches the chicken as its being cooked. Flip and cook on the other side and continue swirling the pan until the chicken is golden brown.
Remove from the pan and place the chicken on a paper towel-lined plate or sheet pan fitted with a wire rack. Repeat with the remaining chicken cutlets.
Serve with potato salad, a fresh salad, or mashed potatoes, lemon wedges (squeeze a little before eating), and a sprinkle of freshly chopped parsley.