In a small bowl, mix together honey, cayenne, 1 teaspoon of pimenton, and 1/2 teaspoon of salt. Cover the bowl and leave it at room temperature for up to 1 day. This will be poured on the fried chicken when it's done.
In another bowl, whisk together buttermilk, garlic, the remaining 3 teaspoons of pimenton, and 2 tablespoons of salt. Pour this mixture into a large resealable plastic bag, add the chicken, close the bag, and turn it to coat the chicken. Put the bag in the refrigerator for at least 4 hours, preferably overnight.
Take the chicken out of the refrigerator 1 to 2 hours before cooking to bring it to room temperature.
In a large baking dish, whisk together flour, cornstarch, and 1 teaspoon of salt.
Pour 1/2 inch of oil into a large heavy pot over medium heat and let it heat up.
Meanwhile, take the chicken out of the bag, let the excess buttermilk drip back in, then place the chicken into the flour mixture. Lightly coat each piece on all sides and transfer to a plate. Get rid of the excess buttermilk and flour mixtures.
When the oil is hot (it bubbles around the chicken when a piece is dripped into it), use tongs to gently and carefully place a few pieces in the oil without crowding them. The number of pieces depends on the size of your pot.
Cook the chicken, turning it every few minutes and adjusting the heat as needed, until the skin is dark golden brown and the chicken is firm to the touch. An instant-read thermometer inserted in the thickest part of the chicken should register 170°F. This will take about 15 minutes for wings and breast pieces, and 18 to 20 minutes for legs and thighs. Place the cooked chicken on a serving platter lined with paper towels. Keep frying the remaining pieces, adding more oil to the pot if needed.
Serve the freshly fried chicken right away with the honey mixture for drizzling and dipping. It's tasty at room temperature and surprisingly delicious when cold.