To make the chicken shake, mix all of the ingredients together in a bowl.
To make the fried chicken, put 480ml/17fl oz water and the salt in a saucepan over a high heat and bring to a simmer, stirring to dissolve the salt. Pour into a large heatproof container, pour in 1.4 litres/2½ pints water and leave to cool to room temperature. Add the chicken thighs and drumsticks, cover and chill in the fridge for 1½ hours. Drain and pat the chicken dry with a teatowel or kitchen towel.
Whisk the buttermilk, coconut milk, garlic and chicken shake together in a 23x33cm/9x13in baking dish. Submerge the chicken in the marinade, cover, and chill in the fridge overnight.
Fill a large saucepan one-third full with peanut oil. Set over a medium–high heat and heat to 180C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Put the flour, semolina, cornstarch and white pepper into a bowl and mix to combine. Remove the chicken pieces from the marinade, letting any excess marinade drip off. Roll the chicken in the flour mixture, coating it fairly thickly. Place on a wire rack set over a baking sheet. If the coating looks wet, roll in the flour again.
Working in batches, fry the chicken until deep brown and it has an internal temperature of 74C when tested with a meat thermometer. This should take about 10 minutes per batch. Keep an eye on the heat to ensure the oil is a stable temperature. Transfer the chicken to drain and cool slightly on the rack set over a baking sheet. Deep-fry the rosemary and add to the chicken.
To make the hot honey glaze, heat all of the ingredients in a small saucepan until warmed through. Toss the fried chicken in the hot honey glaze.
Meanwhile, to make the pumpkin and Bruseels sprouts, preheat the oven to 200C/180C Fan/Gas 6. Place the pumpkin and sprouts in a roasting tin, drizzle with the olive oil and season with salt. Roast for 30–40 minutes, or until softened and cooked through.
Melt the butter in a saucepan and cook until just turning brown. Add the apples, garlic, star anise and 4 tablespoons of water. Cover and cook until the apples are soft. Remove the star anise, add the pumpkin and sprouts, cranberries, parsley and sage and mix well. Season with salt and pepper.
Serve the chicken with the pumpkin and Brussels sprouts on warmed plates.