1. MAKE THE CHICKEN: Add the chicken and buttermilk to a bowl with a lid or to a large food storage bag and seal. Set on the counter to marinate for 1 hour or place in the refrigerator for longer, up to overnight. If you don’t have even an hour to spare for marinating, you can use the buttermilk as a dip before dredging the meat in flour, skipping this step altogether. The chicken will not be quite as tender, but it will still be juicy and delicious.
2. When ready to cook, prepare your frying station: Set a cooling rack on top of a large sheet pan next to the stove. Pour enough oil into a large pot so that it comes 1 inch up the sides. Clip a frying thermometer to the side of your pot.
3. Whisk together the flour, corn- starch, garlic powder, salt, black pepper, and cayenne in a wide, shallow bowl. Start heating the oil over medium-high heat as you dredge the chicken in the flour mixture to coat well. (I like to do this in batches as the oil is ready so that the coating doesn’t get wet before frying from sitting too long on the chicken.)
4. Once the oil reaches around 360°F (180°C), shake excess flour off of a couple of chicken pieces and drop them in the oil, being careful not to overcrowd the pot (I fry in a pot that is 12 inches in diameter and cook two thighs at a time). Fry for 5 minutes, using tongs to carefully flip the pieces halfway through.
Note: You’ll need a frying thermometer to monitor the heat of the oil.
Transfer the fried chicken to the cooling rack, and allow it to rest for 5 minutes. Repeat until all pieces are done. If desired, lightly dab the chicken with paper towels to soak up any excess oil before serving.
5. MAKE THE SANDWICHES: To make the sauce, whisk together the mayonnaise, chives, pickle brine, and mustard. If not assembling the sandwiches right away, set the sauce aside in the refrigerator.
6. Toast the rolls and butter both sides. Slather the top half of each roll with sauce. Place a chicken thigh on the bottom half of each roll and top with lettuce, sliced tomato, and dill pickle. Add the top half and serve immediately.