Prepare the Chicken: Place each chicken breast between two pieces of plastic wrap and pound with a meat mallet until thin. Mix flour, salt, and pepper in a bowl. In another bowl, whisk together eggs and milk.
Cook the Chicken: Heat olive oil in a large pan over medium-high heat. Dredge each chicken cutlet in the flour mixture, then dip into the egg mixture. Cook for 4 minutes per side or until golden brown and cooked through. Remove chicken and keep warm.
Make the Sauce: In the same pan, melt 1 tablespoon of butter, add lemon slices and cook until browned. Remove slices. Add remaining butter, melt, and then stir in flour. Cook for one minute, add white wine and simmer for 2 minutes. Add chicken broth and simmer until the sauce thickens slightly.
Finalize: Stir in lemon juice, season with salt and pepper. Return chicken to pan, coat with the sauce, top with lemon slices and parsley, and serve.
