Place the chicken thighs and drumsticks, the head of garlic (if using) and thyme sprigs (if using) into a large pan and cover with cold water.
Bring the water to the boil, then reduce the heat until the water is simmering. Continue to simmer for 25-30 minutes, or until the chicken pieces are cooked through.
Remove the pan from the heat and set aside. When the chicken has cooled, in the stock, chill, covered, in the fridge until needed (but no longer than overnight).
In a bowl, mix together the flour, ground cumin, cayenne pepper, celery salt, mustard powder and salt until well combined.
Remove the chilled chicken pieces from the stock using tongs and pat dry with kitchen paper. Remove the skin if desired. (The remaining cooking liquid can be reserved in the fridge for up to three days and used as stock in another recipe. Alternatively, it can be frozen until needed.)
Dredge the chicken pieces in the spiced flour until coated.
Pour the milk into a bowl and dip each floured chicken piece into it until covered.
Dredge the chicken pieces in the spiced flour for a second time. (NB: Double-coating the chicken pieces will make them extra crisp.)
Pour the vegetable oil into a large pan until it reaches 10cm/4in up the sides of the pan. (CAUTION: Do not over-fill the pan - the pan should only be half full with oil. Hot oil can be dangerous. Do not leave unattended.)
Heat the oil to 170C (use a cooking thermometer to test the temperature - alternatively, heat the oil in a deep fat fryer). When a breadcrumb dropped into the oil sizzles and turns golden-brown, gently lower the chicken pieces, in batches, into the hot oil using a slotted spoon.
Fry for 4-5 minutes, or until crisp, golden-brown and completely cooked through. Remove the chicken pieces from the pan using a slotted spoon and set aside to drain on kitchen paper. Keep warm.
Repeat the process with the remaining chicken pieces.
Cut the chilled baked potatoes into wedges, pat dry with kitchen paper, then lower them, in batches, into the hot oil. Fry for 2-3 minutes, or until crisp and golden-brown. Remove from the pan using a slotted spoon and set aside to drain on kitchen paper. Keep warm.
Repeat the process with the remaining potato wedges.
Meanwhile, in a bowl, mix together all of the vegetables and the mayonnaise until the mixture is well combined and resembles coleslaw.