Boil 1 litre of water with salt, demerara sugar, bay leaves, thyme, star anise, and lemon rind until dissolved.
Submerge the pork shoulder in the cooled brine and refrigerate for 24 hours.
Preheat the oven to 140°C.
Pat the pork dry, drizzle with oil, wrap tightly in foil, and slow cook in a roasting tin for four hours.
Let the wrapped meat rest for 30 minutes.
Simmer vinegar, stock, brown sugar, wine, garlic, honey, and bay leaves in a pan.
Shred the pork with forks and simmer in the stock for 40 minutes until glazed.
Blend egg yolks, mustard, and vinegar in a food processor until smooth.
Emulsify by adding vegetable and walnut oils slowly, then season and stir in walnuts.
Combine carrot, cabbage, and onion with some of the walnut mayonnaise to make coleslaw.
Season the glazed pork with lemon juice, fresh tarragon, salt, and pepper.
Fill toasted pitta breads with coleslaw, pulled pork, and optional lettuce.