Begin by placing the chicken breasts between two sheets of plastic wrap. Use a meat mallet or a rolling pin to pound the chicken to an even thickness, about ½ inch.
Season the chicken breasts with salt and black pepper on both sides. In one shallow bowl, place the all-purpose flour. In a second shallow bowl, whisk together the egg and water. In a third bowl, combine the breadcrumbs with a pinch of salt. Dredge each chicken breast first in the flour, shaking off the excess, then dip into the egg wash, and finally coat with the breadcrumbs.
In a large skillet, heat the olive oil and butter over medium heat. Add the breaded chicken breasts and cook for about 4-5 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chicken broth, scraping up any browned bits from the bottom. Stir in the lemon juice and zest, and bring to a simmer. Cook for about 2-3 minutes to reduce slightly.
Lower the heat and stir in the heavy whipping cream and capers. Let the sauce simmer for an additional 2-3 minutes until it thickens slightly. Adjust seasoning with more salt and pepper if needed.
Return the chicken to the skillet, spooning the sauce over the top. Allow everything to warm through for about 1-2 minutes, then remove from the heat.
Serve your Creamy Lemon Chicken Piccata over hot cooked pasta or a mound of mashed potatoes. Drizzle extra sauce on top and garnish with fresh parsley or lemon slices if desired.