01 - Combine the 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 full 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 all surfaces 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 rimmed baking sheet.
07 - Roast in the preheated oven for 1 hour, or until a meat thermometer inserted into the center registers 162°F.
08 - Remove the meat from the oven and let it cool completely at room temperature, then refrigerate—preferably overnight—before slicing thinly for sandwiches.