Chicken Cutlets: take 3 boneless, skinless chicken breasts and cut in half lengthwise to create two thin cutlets (these will cook faster and more evenly than whole chicken breasts). Season each cutlet with a little kosher salt and ground black pepper; set aside.
Prep Cutlets: In a medium bowl, combine ⅔ cup all-purpose flour, 2 teaspoons garlic powder, 2 teaspoons onion powder and 2 teaspoons Italian seasoning. Stir to combine. Taking chicken cutlets one at a time, place them in the flour mixture and ensure each piece is fully coated. Place coated chicken cutlets on plate; set aside. Discard flour mixture.
Sear Chicken: Bring large cast iron skillet to medium high heat. Add 1 tablespoon butter and 1 tablespoon extra virgin olive oil. Let butter melt and then, in batches, cook chicken cutlets 1-3 minute per side or until chicken is light golden brown. Place chicken on a clean plate; set aside.
Sauce: Add remaining 2 tablespoons of butter to the pan along with the 2 tablespoons shallot and 1 tablespoon garlic. Sauté for 1-2 minutes. Add 1 ½ cups chicken broth, 2 tablespoons white wine, 2 tablespoons fresh lemon juice, 2 tablespoons capers, 1 tablespoon lemon zest, and 1 lemon (sliced). Let simmer until reduced by half - about 5-6 minutes. Nestle chicken back into the pan and bring to a gentle simmer for 5-10 minutes or until chicken is cooked through.