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