In a large bowl or pot, combine the cold water, salt, sugar, crushed peppercorns, smashed garlic, and hot sauce (if using). Stir until the salt and sugar are completely dissolved.
Add the chicken pieces to the brine, making sure they are fully submerged. You might need to weigh them down with a plate.
Cover the bowl or pot and refrigerate for at least 4 hours, or preferably overnight (but no more than 24 hours).
In a large bowl, whisk together the flour, cornstarch, paprika, garlic powder, onion powder, thyme, oregano, cayenne pepper, black pepper, salt, baking powder, and baking soda.
In a separate bowl, whisk together the eggs, buttermilk (or milk mixture), and hot sauce (if using).
Remove the chicken pieces from the brine and pat them completely dry with paper towels.
Set up a breading station: place the flour mixture in one shallow dish and the egg wash in another.
Dredge each piece of chicken in the flour mixture, making sure it's fully coated. Then, dip it into the egg wash, allowing the excess to drip off. Finally, dredge it again in the flour mixture, pressing gently to ensure the batter adheres well.
Heat the vegetable shortening, peanut oil, or canola oil in a large, heavy-bottomed skillet or Dutch oven over medium-high heat to 325-350°F (160-175°C). Use a deep-fry thermometer to monitor the temperature.
Carefully place a few pieces of chicken in the hot oil, making sure not to overcrowd the pan.
Fry the chicken for about 6-8 minutes per side, or until it's golden brown and the internal temperature reaches 165°F (74°C). Use a meat thermometer to check the temperature.
Remove the fried chicken from the skillet and place it on a wire rack lined with paper towels to drain excess oil.
Repeat with the remaining chicken pieces, maintaining the oil temperature.
Let the chicken cool slightly before serving.