01 - Combine cold water, kosher salt, and sugar in a large mixing bowl, stirring until fully dissolved.
02 - Submerge the chicken or turkey breast in the brine, cover the bowl, and refrigerate for 4 to 8 hours.
03 - Set the oven to 325°F and allow it to come to temperature.
04 - Remove the meat from the brine and pat it thoroughly dry with paper towels. Combine the black pepper, garlic powder, onion powder, smoked paprika, and dried thyme, then rub the seasoning blend evenly over the entire surface of the meat.
05 - Roll the seasoned meat tightly in parchment paper, then wrap it securely in aluminum foil, twisting both ends firmly to form a compact log shape.
06 - Place the wrapped meat log on a wire rack set inside a baking sheet.
07 - Roast for 1 hour, or until a meat thermometer inserted into the center registers 162°F.
08 - Remove from the oven and allow the meat to cool completely, preferably refrigerating it overnight, before slicing thinly for sandwiches.