Preheat your oven to 375°F (190°C).
Take the chicken breasts and place them in a large Ziplock bag or between two sheets of plastic wrap. You need to Pound each one with the flat side of a meat mallet until they're about 1/4 inch thick, then season both sides with salt and pepper.
In a shallow dish, mix together some flour, 1 teaspoon of salt and 1/2 teaspoon of pepper. Whisk an egg and water together in another shallow bowl and put breadcrumbs in a third one. Dip the chicken breasts into the flour mixture, shaking off any excess that sticks to them before dipping them into the egg mixture and coating with breadcrumbs.
In a large pan, heat 2 tablespoons of olive oil over medium-high heat until shimmering. Fry the chicken breasts for about 3 minutes on each side until they are golden brown and then transfer them to a baking sheet lined with parchment paper or a baking mat. Pop them into the preheated oven and bake for 10 to 12 minutes, or until cooked through.
While the chicken is in the oven, add 1 tablespoon of butter and another tablespoon of olive oil to the same pan on medium heat. Place the reserved lemon halves cut side down into the hot oil and cook until golden brown (about 3 minutes). Remove them from the pan afterwards and discard.
Finally, add 2 more tablespoons of butter to the pan get it melted, then pour in the lemon juice, white wine, 1 teaspoon of salt and 1 teaspoon of pepper. Simmer for 3 to 4 minutes until the sauce has reduced slightly.
Serve up the chicken piccata on a platter with the sauce poured over it and top with some sliced lemons and chopped parsley for garnish.