Butterfly the chicken breast ( hold a long knife along the thicker part of the breast and cut almost through and open like a book. Place some plastic wrap over top and pound to flatten to about 1/2 inch.
Place the eggs into a dish large enough to fit the chicken breast. Season the eggs with salt and pepper. Add the parsley and parmesan cheese. Mix well.
Place flour in another dish. Add the olive oil and half the butter to a large skillet. Coat the chicken in flour shaking off the excess. Dip in the egg wash Fry about 4 minutes each side depending on how thick.
Remove chicken to a plate. Add the wine to the pan. Let reduce to about half. Add the chicken stock, garlic and lemon juice. Add the remaining butter. Add the chicken back to pan and cook a couple of minutes.