In a shallow bowl, mix together flour, 1 teaspoon salt, and 1/2 pepper. Set aside.
Beat the eggs in a second shallow bowl. Set aside.
Dry the chicken of any moisture with paper towels.
Heat the oil in a 12 inch, high sided skillet, over medium heat. While the oil is heating, dredge 2 chicken breasts in flour mixture, shaking off excess. When oil begins to shimmers, dip the 2 floured breasts in egg mixture and coat both sides, allowing excess to drip off, then add to the skillet.
Repeat with 2 remaining breasts. Cook breasts, until golden brown, flipping over once (coating is delicate) until the chicken is cooked through, approximately 4-6 minutes. Remove cooked chicken to a paper towel-lined plate and tent loosely with aluminum foil to keep warm.
Pour out and throw away oil from the skillet. Wipe the skillet out with paper towels.
Add the butter to the skillet and heat over medium-low, until butter is melted and foam subsides.
Pour in the wine, broth, and fresh lemon juice and continue to cook, stirring occasionally, until the sauce is reduced to 1 cup, about 7-9 minutes. Stir in remaining 1/4 teaspoon salt and 1/4 teaspoon pepper, and parsley. Ladle sauce over chicken and garnish with lemon slices. Serve