01 - In a large bowl or resealable plastic bag, combine the dill pickle juice, sugar, and whole peppercorns. Add the chicken breasts, seal tightly, and refrigerate for at least 1 hour or up to 4 hours.
02 - Preheat the oven to 400°F if baking the chicken rolls.
03 - Remove the chicken from the brine and pat dry with paper towels. Butterfly each breast by slicing horizontally almost all the way through, then opening it like a book. Place each piece between two sheets of plastic wrap and pound to ¼-inch thickness using a meat mallet.
04 - Layer one slice of cheese, one slice of ham (if using), and a generous sprinkle of fresh herbs onto each pounded breast. Season lightly with salt and pepper. Roll each breast tightly, tucking in the sides, and secure with toothpicks.
05 - Arrange three shallow bowls: one with flour, one with beaten eggs, and one with panko breadcrumbs mixed with garlic powder and smoked paprika.
06 - Dredge each rolled chicken breast in flour, shaking off excess. Dip into the beaten eggs, then coat thoroughly in the seasoned panko mixture, pressing gently to adhere.
07 - For frying: Heat oil in a large skillet over medium heat. Fry the chicken rolls, turning every 3–4 minutes, until all sides are golden brown. Transfer to a baking sheet and finish in the oven for 15 minutes, or until cooked through to an internal temperature of 165°F. For baking only: Arrange the rolls on a parchment-lined baking sheet, drizzle with melted butter or oil, and bake for 25–30 minutes until golden and cooked through.
08 - Let the chicken rolls rest for 5 minutes. Remove toothpicks, slice into pinwheels, and serve hot.