Prepare the chicken breast and set aside on a plate. Add the flour to a shallow dish or pie plate, and season with salt and pepper to taste. Mix with your hands to combine. In another shallow dish, beat the eggs with 2 tablespoons water.
Meanwhile, heat the olive oil in a cast iron skillet over medium high heat. Season the chicken with salt and pepper, and then dredge the chicken in the seasoned flour. Dip them in the egg wash to coat completely, letting the excess drip off. When the oil is nice and hot, add the cutlets and fry for 4 minutes on each side until golden, turning once. Remove the chicken cutlets to a plate and set aside.
Toss the lemon slices into the pan and cook for 1 to 2 minutes, until fragrant. Add the garlic, wine, broth, and lemon juice, and simmer for 5 minutes to reduce the sauce slightly, stirring often. Reduce the heat to medium low and add the butter.
Return the chicken to the pan, and place the lemon slices on top of the cutlets. Simmer gently for 2 minutes to heat the chicken through. Season with salt and pepper and garnish with chopped parsley before serving with pasta or rice.
