Season the chicken with salt and pepper. Combine the flour, Parm, salt, pepper, and Italian seasoning and mix. Dredge the chicken in the flour mixture, shaking off the excess, and add to a plate.
Add the olive oil to a skillet over high heat. Once hot, sear the chicken until golden on each side (about 1-2 minutes), and then remove to a plate.
Lower the heat to medium-low. Allow the pan to cool a bit, then add the garlic and capers. Cook for about 1 minute, and then deglaze with the wine. Bring the heat up to medium and let cook until the wine has almost completely reduced.
Add the chicken stock, lemon juice, and lemon zest to the pan. Bring to a simmer, and then add the chicken and their juice back to the pan. Let simmer until the chicken is cooked through, about 5-10 minutes, depending on how thick the chicken is. Once done, remove the chicken to a plate and shut the heat. (If the sauce hasn't thickened to your liking, you can reduce a bit more before shutting the heat.)
Finish the sauce by adding the cold butter and swirling it in. Once melted, add the chicken back to the pan. Spoon the sauce on top and garnish with fresh parsley.