Preheat the oven to 350 degrees.
Heat the oil in a large, heavy pot (deep enough so that the oil is no more than halfway up the sides and wide enough to hold 2-3 pieces of chicken at once) until the oil reaches 360 degrees.
Remove buttermilk and chicken from refrigerator and let it come as close as possible to room temperature.
Combine flour, salt, black pepper, cayenne, granulated garlic, and granulated onion in a broad, shallow dish. Mix well.
Drain the chicken pieces well.
Add the chicken, one piece at a time, to the seasoned flour and coat well.
Carefully add chicken, in batches of 2 or 3 pieces, to the hot oil.
Cook each batch until golden brown, turning once. (For the first batch, this usually takes about 4 minutes for the first side and 3 for the other side.)
Set a large cooling rack on a cookie sheet with sides. Remove cooked chicken from oil and place on rack.
Let oil temperature return to 360 degrees.
Repeat with the rest of the chicken, letting the oil heat up again between batches. (*Important note:* each batch will take less time to reach the desired color than the one before, so watch carefully!)
When all chicken pieces have been deep-fried and placed on the rack, place the cookie sheet and cooling rack in the hot oven. Bake for 30 minutes, checking once or twice. Do not let the breading get too dark.
Serve hot or at room temperature.