01 - In a large bowl or resealable plastic bag, combine the pickle juice, sugar, and peppercorns. Add the chicken breasts, seal or cover, and refrigerate for at least 1 hour or up to 4 hours.
02 - Preheat oven to 400°F if baking. Line a baking sheet with parchment paper and set aside.
03 - Remove the chicken from the brine and pat dry with paper towels. Butterfly each breast by slicing horizontally almost all the way through and opening it like a book. Place each butterflied breast between two sheets of plastic wrap and pound to ¼-inch thickness using a meat mallet or rolling pin.
04 - Layer a slice of cheese, a slice of ham if using, and a sprinkle of chopped herbs onto each flattened breast. Season lightly with salt and pepper. Roll each breast up tightly, tucking in the sides, and secure with toothpicks.
05 - Arrange three shallow bowls: 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 frying: heat oil in a large skillet over medium heat. Fry the chicken rolls, turning occasionally, until golden brown on all sides, about 3 to 4 minutes per side. Transfer to the prepared baking sheet and bake for 15 minutes, or until cooked through to an internal temperature of 165°F. For baking only: place the rolls on the parchment-lined baking sheet, drizzle with melted butter or oil, and bake for 25 to 30 minutes until golden and cooked through.
08 - Let the chicken rolls rest for 5 minutes. Remove toothpicks, slice into pinwheels, and serve hot.