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Before handling the duck breasts, make sure to remove them from the refrigerator and let them sit for 10 minutes. Otherwise, the transition between cold and very hot will make the meat less tender.
LIGHTLY score the skin of the duck breasts, then season with salt and pepper. SHRED the green cabbage and dice the celeriac. CRUSH the walnuts and set them aside.
HEAT UP the skillet on medium-low heat, add in the duck breasts without anything else. You'll soon notice fat starting to come out from the duck, this is exactly what we want.
Add in the garlic clove, with skin on and a few sprigs of fresh thyme. Don't move, stir the duck breasts; just let it cook for about 15 to 20 minutes on low heat. (pictured below). In a way, we're cooking duck as we would cook fish.
While the duck cooks, work on the cabbage. When the duck skin becomes crisp and brown, flip the duck over to cook on the flesh side for 3 minutes, or until browned.
You'll end up with delicious, tender pink duck meat. You can cook it a little bit longer if you prefer. (pictured below).
While the duck breasts are cooking heat up 1 tablespoon of duck fat in the other pan/skillet with some olive oil. Put the pan on medium-high heat. ADD in diced celeriac and gently fry for about 5 minutes, until the celeriac has slightly browned.
Add thyme, white wine vinegar to your liking along with the shredded green cabbage. Turn up the heat and fry the cabbage for about 5 minutes, or until it starts to wilt. ADD 100 ml water and let simmer for 5 minutes, until the water has been evaporated.
The celeriac should be soft by now. POUR in 100 ml double cream, stir to coat all of the vegetables. ADD in crushed walnuts. Lastly, put the icing sugar / powdered sugar in the non-stick small saucepan.
Gently heat up to make a light amber caramel. POUR in vinegar and wait for it to become a sticky syrup. SLICE each pear in halves, use a melon baller or teaspoon to scoop out the core. PLACE star anise in the cavity of each pear half.
DUST using more icing sugar or powdered sugar. PLACE into the pan on medium-high heat, cook the pear halves for 10 minutes or until brown and caramelised. SCOOP over some of the hot syrup while cooking.
Make more syrup while cooking, if needed. SPOON a neat mound of creamed cabbage in the middle of the plate, place the (sliced) duck breast against it and add 1 or 2 pear halves on the other side.
DRIZZLE remaining sticky syrup on the plate, serve immediately.