Start by removing the spine of the duck (spatchcock or butterfly it). If you’re not sure how to do this, here is a helpful video on how to butterfly a duck.
Prick the skin all over and use a sharp knife to lightly score the skin on the breast side, making sure not to cut the meat.
Coat the duck in salt and let it sit, uncovered, in the fridge overnight.
Heat a sous vide water bath to 150F degrees.
Combine the remaining ingredients (except fennel and green onions) in a bowl and mix to combine.
Coat the duck in the sauce and place in a vacuum seal bag (or ziplock bag if using the water displacement method) with the fennel and green onion. Seal the bag.
Place it in the water bath and let it cook for 12 hours.
Remove the duck from the water bath and the bag (reserve the bag juice) and place on a roasting rack.
Roast in a 450F degree oven for 15-30 minutes, or until the skin has turned a golden brown. Be careful not to over-roast as the duck could dry out.
While the duck roasts, place the bag juice in a saucepan and simmer, skimming the fat and particles off the top as it cooks. Adjust the taste with salt.
Remove duck from the oven and let cool slightly. Carve and serve it drizzled with the cooked bag juice.