Start by pounding the chicken breasts between two pieces of plastic wrap until they are about 1/4-inch thick. Season both sides with salt and pepper.

In a shallow dish, whisk together the flour, salt, and pepper. In another shallow dish, beat the eggs and mix in the grated Parmesan cheese.

Dip each chicken breast into the flour mixture, shaking off any excess. Then dip it into the egg mixture, making sure it's coated evenly.

Heat the olive oil and 2 tablespoons of butter in a large skillet over medium-high heat. Once the butter has melted and the skillet is hot, add the chicken breasts. Cook for about 3-4 minutes per side, until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.

In the same skillet, add the remaining 2 tablespoons of butter, chicken broth, lemon juice, and white wine. Stir well and bring to a simmer. Cook for 2-3 minutes, allowing the sauce to thicken slightly and the alcohol in the wine to cook off.

Return the cooked chicken breasts to the skillet, coating them with the sauce. Cook for an additional 2 minutes, allowing the flavors to meld together.

Serve the Chicken Francese immediately while it's hot. It pairs well with pasta, rice, or a side of steamed vegetables. Garnish with lemon slices and fresh parsley if desired. Enjoy!