In a small bowl, combine paprika, black pepper, garlic powder, oregano, and cayenne. Mix thoroughly.
In a large bowl, whisk together buttermilk, egg, salt, and 2 tablespoons of the spice mix. Add the chicken pieces, ensuring they're fully coated. Transfer to a gallon-sized zip-top bag, refrigerate for at least 4 hours or overnight, flipping occasionally.
In another large bowl, whisk flour, cornstarch, baking powder, 2 teaspoons of salt, and the remaining spice mix. Add 3 tablespoons of marinade from the chicken bag and incorporate it into the flour mixture with your fingers.
Remove the chicken from the bag one piece at a time, letting excess marinade drip off. Coat each piece in the flour mixture, pressing firmly to create a thick, even layer.
Preheat your oven to 350°F and set a wire rack over a baking sheet.
In a deep skillet or cast-iron pan, heat shortening or oil to 425°F. Adjust the heat to maintain 300°F while cooking. Fry chicken skin-side down for 6 minutes without moving, then carefully flip and cook for 4 more minutes.
Transfer cooked chicken to the wire rack and bake until breast pieces reach 150°F and thighs/drumsticks reach 165°F, about 5-10 minutes.
For extra crispiness, refrigerate the cooked chicken for at least 1 hour, then fry again at 400°F for 5 minutes before serving.