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 oven to 400°F. Line a baking sheet with parchment paper if baking.
03 - Remove 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 butterflied breast between two sheets of plastic wrap and pound to an even ¼-inch thickness using a meat mallet or rolling pin.
04 - Layer one slice of cheese, one slice of ham if using, and a sprinkle of chopped fresh herbs onto each pounded breast. Season lightly with salt and pepper. Roll each breast up tightly, tucking in the sides, and secure with toothpicks to hold the shape.
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 rolled chicken breast in flour, shaking off excess. Dip into the beaten eggs, then press firmly into the seasoned panko breadcrumbs, coating all sides thoroughly.
07 - For frying: Heat oil in a large skillet over medium heat. Fry the chicken rolls, turning carefully, until golden brown on all sides, about 3 to 4 minutes per side. Transfer to the prepared baking sheet and finish in the oven for 15 minutes, or until the internal temperature reaches 165°F. For baking only: Arrange rolls on the parchment-lined baking sheet, drizzle with melted butter or oil, and bake for 25 to 30 minutes until golden brown and cooked through to 165°F.
08 - Let the chicken rolls rest for 5 minutes. Remove toothpicks, slice into pinwheels, and serve hot.