Preheat oven to 200 degrees F. Place a baking sheet in oven to keep cooked cutlets crisp.
Butterfly the chicken breast pieces across the breast but not all the way through, open the meat up and set into a plastic food storage bag or 2 pieces waxed paper. Gently pound out each piece into very thin, large cutlets. Pile cutlets on a plate and season with salt and pepper.
Arrange a station for breading: flour, 2 beaten eggs, bread crumbs mixed with paprika, parsley and the zest of a lemon.
Heat just enough oil to coat the bottom of a large nonstick skillet over medium to medium-high heat.
Bread 2 cutlets in flour, then egg, then bread crumb mixture and cook 2 to 3 minutes on each side, transfer to oven, add a bit more oil, if necessary, and repeat. Keep the cooked cutlets hot in the warm oven. Wipe pan clean, add 1 tablespoon extra-virgin olive oil heat then add roasted red peppers, season with salt and pepper and wilt them 4 to 5 minutes.
While cutlets are in oven and peppers are cooking up, heat 1 tablespoon of butter in a medium skillet over medium heat. Add 4 eggs and fry to desired doneness, season with salt and pepper.
Arrange some lettuce on each dinner plate, top with 1 cutlet, and some of the lemon juice over top. Arrange some roasted red pepper strips, 2 anchovy fillets, 1 tablespoon capers and a fried egg, sunny-side up or over easy on top of the cutlets. Serve with lemon wedges.