Place the chicken breasts between two sheets of plastic wrap or parchment paper.
Using a meat mallet or rolling pin, gently pound the chicken until it’s about ½ inch thick.
Season both sides with salt and pepper.
In a shallow bowl, whisk the eggs together with the Parmesan cheese.
Place the flour in another shallow bowl and season it lightly with salt and pepper.
Heat the olive oil and 2 tablespoons of butter in a large skillet over medium-high heat.
Dredge each chicken breast first in the flour, making sure to shake off excess, then dip it into the egg mixture, coating both sides.
Carefully place the chicken in the hot skillet and cook for 3-4 minutes on each side until golden brown and fully cooked through. Transfer the cooked chicken to a plate and cover to keep warm.
In the same skillet, add the white wine (if using) and chicken broth, scraping the browned bits from the bottom of the pan. Let it simmer for 2 minutes.
Add the lemon juice and the remaining butter to the pan. Stir the sauce as the butter melts to create a creamy texture. Let it simmer for another minute.
Return the chicken breasts to the skillet, spooning the lemon-butter sauce over them.
Let the chicken simmer in the sauce for 2-3 minutes so the flavors meld together.
Sprinkle chopped parsley over the top and add lemon slices for garnish.
Plate the Chicken Francese, spooning extra sauce over the top
Serve with your favorite sides like pasta, mashed potatoes, or steamed vegetables