01 - In a large bowl or resealable plastic bag, combine the dill pickle juice, granulated sugar, and whole black peppercorns, stirring until the sugar dissolves.
02 - Submerge the chicken breasts in the brine mixture, seal or cover, and refrigerate for at least 1 hour and up to 4 hours for optimal flavor penetration.
03 - If baking, preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
04 - Remove the chicken from the brine and pat thoroughly dry with paper towels. Butterfly each breast by slicing horizontally almost completely through, then opening it like a book. Place each piece between two sheets of plastic wrap and pound to an even ¼-inch thickness using a meat mallet.
05 - Layer one slice of cheese, one slice of ham if using, and a generous sprinkle of chopped herbs onto each flattened breast. Season lightly with salt and freshly ground black pepper. Roll each breast up tightly, tucking in the sides, and secure with toothpicks.
06 - Arrange three shallow bowls: the first with all-purpose flour, the second with beaten eggs, and the third with panko breadcrumbs mixed with garlic powder and smoked paprika.
07 - Dredge each rolled chicken piece in flour, shaking off excess, then dip into the beaten eggs, and finally coat thoroughly in the seasoned panko mixture, pressing gently to adhere.
08 - For the pan-fried method, heat vegetable oil in a skillet over medium heat and fry the rolls, turning every 3–4 minutes, until all sides are golden brown. Transfer to the prepared baking sheet and finish in the oven for 15 minutes or until the internal temperature reaches 165°F (74°C). For baking only, place the rolls on the parchment-lined sheet, drizzle with melted butter or oil, and bake for 25–30 minutes until golden and cooked through.
09 - Allow the chicken rolls to rest for 5 minutes before slicing. Remove toothpicks, cut into pinwheel slices, and serve hot.