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Heat the oven to 120C/100C fan/gas ½. Scatter the lemon slices, thyme sprigs and reserved dill stalks over the base of a large, shallow roasting tin or baking tray. Season the salmon generously with salt and pepper and rub half the olive oil all over the fish. Lay the salmon skin-side up on top of the lemon and herbs. Roast for 45-50 mins until the fish feels firm and a corner of skin peels away easily. If you have a digital thermometer, the salmon should be at about 55C when ready. Leave to cool slightly in the tin.
While the salmon is cooking, tip the potatoes into a pan of cold salted water and bring to the boil. Reduce the heat to a simmer and cook for 10-15 mins until just tender. Drain. Mix the mustard, lemon juice and olive oil together in a large bowl, and season with salt and pepper. Tip the hot potatoes into the bowl and toss to coat in the dressing. Set aside. Can be served hot or made a day ahead and chilled.
Carefully lift the salmon onto a serving platter, if you like (it can also be served directly from the tin). Peel away and discard the skin, then use a cutlery knife to neatly scrape away the grey meat on top (see quick fishcakes recipe, below, to use it up), leaving the pink flesh underneath. The salmon is now ready to eat warm, or leave to cool completely and eat at room temperature. (See tip for garnishing the salmon, below.) Will keep chilled for up to two days. Can be served cold.
For the mayonnaise, mix all of the ingredients together in a small bowl. Can be made a day ahead and kept chilled. Just before serving, brush the rest of the olive oil over the salmon and season with sea salt. Serve with the potato salad and dill & mustard mayonnaise on the side.