Place the chicken breasts between two sheets of plastic wrap and pound them to an even thickness.
Season the chicken with salt and pepper.
Place the flour in a shallow dish. In another shallow dish, whisk together the eggs, milk, and Parmesan cheese.
Dredge each chicken breast in the flour, shaking off the excess, then dip into the egg mixture, allowing the excess to drip off.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken breasts and cook until golden brown on both sides, about 3-4 minutes per side. Remove the chicken from the skillet and set aside.
In the same skillet, melt the butter. Add the chicken broth, lemon juice, and white wine, scraping up any browned bits from the bottom of the pan. Bring the mixture to a simmer.
Return the chicken to the skillet and simmer in the sauce for about 5 minutes, or until the chicken is cooked through.
Transfer the chicken to a serving platter and pour the sauce over the top. Garnish with chopped parsley.

Variations & Tips
For a gluten-free version, use gluten-free flour for dredging. You can also add capers to the sauce for a briny kick. If you prefer a creamier sauce, stir in a splash of heavy cream at the end. For a touch of heat, add a pinch of red pepper flakes to the sauce. This dish can also be made with veal or pork cutlets for a different twist.