Step 1Wash the game hens or chicken and dry thoroughly. Remove the backbone from each bird (cook with the other pieces, or save for another use), and cut the remaining chicken into 8 pieces (2 breasts, 2 wings, 2 thighs and 2 legs -- 9 if you include the backbone). If the breasts are large, cut each in half crosswise to make a total of 10 pieces.
Step 2In a deep, medium bowl, combine the kosher salt, lemon zest and juice, 1 teaspoon paprika, one-half teaspoon cayenne, the brown sugar, one-half teaspoon garlic powder and one-half teaspoon onion powder and a few dashes of Tabasco to form a rub. Add the chicken pieces to the bowl, massaging the rub all over each piece. Cover the bowl with plastic wrap and refrigerate overnight, or at least several hours.
Step 3The next morning, pour the buttermilk over the pieces and gently toss to coat; the buttermilk should barely cover the chicken; if not, add just enough to roughly cover. Cover the bowl again and refrigerate for 4 to 6 hours for game hen, 6 to 8 for chicken.
Step 4Season the flour: Place the flour, cornstarch and baking powder in a large bag, bowl or baking dish and season with the table salt and one-half teaspoon freshly ground pepper, one-half teaspoon paprika, one-fourth teaspoon cayenne, one-half teaspoon cumin, one-half teaspoon garlic powder, one-half teaspoon onion powder and one-half teaspoon celery salt, or to taste. Taste the flour, and adjust seasoning if desired.
Step 5About 1 hour before frying, remove the bowl from the refrigerator. Remove each piece from the buttermilk, shaking gently to remove any excess buttermilk (do not attempt to dry the pieces). Dredge each piece in the seasoned flour mixture, coating completely. Shake to remove the excess flour, and continue until all of the pieces are coated. Repeat with each of the pieces, so each is floured twice. Set the pieces aside on a rack to dry and warm to room temperature.
Step 6While the pieces are resting, prepare the oil: Place oil in a large, heavy-bottom soup pot or deep fryer to a depth of 3 to 4 inches and heat until the oil reaches 350 degrees.
Step 7Gently place the pieces in the hot oil, being careful not to crowd. Lower the temperature to 325 degrees and fry the pieces until crisp and golden brown and the meat is firm and opaque, about 8 minutes for game hen pieces and 10 to 12 minutes for chicken (timing will vary depending on the size of the pieces); a thermometer inserted in the meat will read 160 degrees when done. Remove the pieces from the hot oil and drain, skin-side up, on crumpled paper towels. Repeat until all the pieces are fried.
Step 8Serve the pieces hot or at room temperature.