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Place the duck breasts, skin-side up, on a board. Score the skin all the way through, cutting down to, but not into, the flesh. Make sure you score all the way to the edges. This will ensure the skin doesn’t pull the flesh in as it shrinks.
Season the skin with a generous amount of salt and freshly ground black pepper. Place the duck, skin-side down, in a solid heavy-based cold pan, then put the pan over a medium heat. Now do not touch anything, do not move the pan. What will happen over the next 10-12 mins is that the fat under the skin will slowly melt, then the skin will brown and go crisp. Once all the fat has run from the skin, there will be a good 1-2cm of duck fat in the pan. Spoon off the excess fat, season the flesh side now (not before), then turn the duck over. Cook for 2 mins, then increase the temperature to full for just 1 min. Take off the heat, then leave in the pan to rest for 5 mins.
For the dressing, put all the ingredients into a small food processor and whizz. Remove the 2 outer leaves from each head of lettuce and discard, then peel the leaves away, one at a time. Lay them out on a big serving plate.
Thinly slice the duck, then toss with the radishes, spring onions, grapefruit, watermelon, herbs and some of the dressing. Spread over the leaves and scatter the nuts over the top. Drizzle more dressing over and serve.