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Lightly score the skin of the duck breasts, then season well. Place a non-stick pan over a medium heat, then lay the duck in the pan, skin-side down. Cook until the fat starts to come from the duck, then add the garlic and thyme. Turn down the heat, then continue to cook for 15-20 mins, depending on the size of the duck breast, until the skin is really crisp and brown. As it cooks, pour the fat into a large pan for the cabbage.
Flip the duck over, cook on the flesh side for 3 mins until browned, then turn off the heat (this will result in meat that is pink in the middle - cook for a few minutes longer if you like it well done). Leave the duck in the pan to rest.
While the duck cooks, heat 1 tbsp of its fat in the other pan. Add the celeriac and bacon, then gently fry for 5 mins until the celeriac has browned and the bacon starts to crisp. Add the thyme, then the cabbage. Fry the cabbage for 5 mins until it starts to wilt. Add 100ml water and simmer for 5 mins until the water has evaporated and the celeriac is soft. Pour in the cream, stir to coat, then add the chestnuts and heat through. This can be done up to a day ahead - cook the celeriac in 1 tbsp vegetable oil instead of the duck fat and reheat with an extra splash of cream before serving.
Cut the pear in half and use a melon baller or teaspoon to scoop out the core. Place a star anise in the cavity of each half.
Place 3 tbsp of the icing sugar in a non-stick pan and heat to make a light amber caramel. Pour in the vinegar and bubble to make a sticky syrup. Dust the pear halves heavily with the rest of the icing sugar, then place the pan back on the heat. Cook the pear for 10 mins until brown and caramelised all over. This can be done up to a day ahead and reheated, adding a splash of water.
To serve, slice each duck breast lengthways and dress the watercress in the olive oil and vinegar. Spoon a neat mound of cabbage on one side of each plate. Place a pear half, cut-side up, on the opposite side of the plate and drizzle the sticky sauce around it. Place the outside slices of duck breast on the cabbage and fan the rest of the duck over. Scatter the dressed watercress sprigs around the sides of the plates and serve.