Butterfly and pound chicken breasts, dry with a paper towel, and season both sides.
Place the flour in a shallow dish. In a second shallow dish, whisk the eggs. Add the breadcrumbs to a third shallow dish.
Dredge each chicken cutlet first in flour, dip it in the egg wash, and then coat it in the breadcrumbs.
Heat olive oil and butter in a pan. Add chicken and cook 3 minutes per side until golden brown.
Transfer cooked chicken to a plate.
Make the sauce in the same skillet by adding the white wine, capers, and lemon juice. Scrape up any browned bits from the bottom of the pan. Bring the sauce to a simmer.
Return chicken to the pan with the sauce and let it simmer. Optional: Keep the chicken warm in a low-temperature oven.
Garnish chicken with parsley and lemon slices. Serve over top of angel hair pasta, using the sauce for noodles.
