01 - In a large bowl or resealable bag, combine the pickle juice, sugar, and peppercorns. Add the chicken breasts and brine for at least 1 hour, up to 4 hours, in the refrigerator.
02 - Preheat the oven to 400°F if baking.
03 - Remove the chicken from the brine and pat dry. Butterfly each breast by slicing horizontally almost through and opening like a book. Place each 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, ham if using, and a sprinkle of fresh herbs on each pounded breast. Season lightly with salt and pepper. Roll up 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 chicken roll in flour, shaking off excess, then dip in beaten egg, and coat thoroughly in the seasoned panko mixture, pressing gently to adhere.
07 - For frying: heat oil in a skillet over medium heat. Fry the chicken rolls, turning occasionally, until all sides are golden brown, about 3 to 4 minutes per side. Transfer to a baking sheet and bake at 400°F for 15 minutes, or until cooked through. For baking only: place rolls on a parchment-lined baking sheet, drizzle with melted butter or oil, and bake at 400°F for 25 to 30 minutes until golden and the internal temperature reaches 165°F.
08 - Let the chicken rolls rest for 5 minutes. Remove toothpicks, slice, and serve hot.