Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper.
Place each chicken breast between 2 sheets of plastic wrap and pound until they are 1/4-inch thick. You can use either a meat tenderizer, or a rolling pin to pound the chicken. Season both sides with salt and pepper.Mix the flour, 1 teaspoon salt, and 1/2 teaspoon of pepper in a shallow plate. In a second plate, beat the eggs and 1 tablespoon of water together. Place the bread crumbs or panko on a third plate. Dip each chicken breast first in the flour, shake off excess, and then dip in the egg and bread crumb mixtures.
Heat 1 tablespoon of olive oil in a large sauté pan over medium heat. Add the chicken breasts and cook for 2 minutes on each side, until browned. Place them on the sheet pan and bake for 5 to 10 minutes while you make the sauce. Because they are so thin, they will cook quickly!
For the sauce, wipe out the sauté pan with a dry paper towel. Who doesn’t love a recipe that uses the same pan without even having to wash it! Over medium heat, melt 2 tablespoons of the butter. Once the butter is melted add the lemon juice, wine, the reserved lemon halves, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Bring to a boil and continue to boil over high heat until reduced in half, about 2 minutes. Remove from the stove, add the remaining 4 tablespoons of butter and swirl to combine.
Discard the lemon halves and serve the chicken on a platter, spoon the sauce over the chicken and garnish with parsley and additional lemon wedges.