Combine the buttermilk, salt and Tabasco in a bowl. Add the chicken pieces and make sure they’re covered by the buttermilk mixture. Cover with cling film and marinate in the fridge for at least 2 hours or preferably overnight (see make ahead).
Heat the oven to 200°C/180°C fan/gas 6. Take the chicken out of the marinade and lightly pat dry with kitchen paper. Combine the flour, cayenne, mustard powder and celery salt, season with salt and pepper, then dip the chicken into the seasoned flour until evenly coated.
Heat 1-2cm oil in a large frying pan until shimmering hot. Add the chicken pieces and fry on each side for 3 minutes until golden. You may need to do this in batches so as not to overcrowd the pan. Remove to a plate thickly lined with kitchen paper.
Put the chicken pieces on a baking sheet, then roast in the oven for 15-20 minutes until cooked through. Serve with coleslaw, if you like.