Make the Garlic Butter: In a medium bowl, mix the butter, garlic, parsley, chives, lemon zest, Parmesan, and salt until well combined.
Transfer the mixture to a sheet of plastic wrap and shape it into a log about 4 inches long. Wrap tightly and freeze until very firm, about 30 minutes.
Prepare the Chicken: Place each chicken breast on a cutting board. Using a small sharp knife, carefully cut a deep pocket into the thickest side of each breast, being careful not to cut all the way through.
Season the chicken inside and out with the salt, garlic powder, onion powder, and black pepper.
Stuff the Chicken: Cut the frozen butter log in half. Stuff one piece into each chicken breast, pushing it deep into the pocket. Press the opening closed as tightly as possible.
Bread the Chicken: Place the flour in one shallow bowl, the beaten eggs in a second bowl, and combine the panko, Parmesan, garlic powder, dried parsley, and paprika in a third bowl.
Dredge each chicken breast in the flour, then dip in the egg, and coat with the panko mixture. For a thicker crust, dip the pocket side back into the egg and breadcrumbs a second time.
Place the breaded chicken on a plate and freeze for 15–20 minutes.
Fry the Chicken: Preheat the oven to 350°F.
Pour enough oil into a large skillet to come about ½ inch up the sides. Heat over medium heat until shimmering.
Fry the chicken for 2–3 minutes per side, or until golden brown. Transfer to a wire rack set over a baking sheet.
Finish in the Oven: Bake for 12–15 minutes, or until the chicken reaches an internal temperature of 165°F.
Let the chicken rest for 5 minutes before serving. Garnish with fresh parsley and serve with lemon wedges for squeezing over the top.