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First, make the dough. Gently warm the butter with the milk in a small saucepan over a low heat until the butter has just melted (but don’t let the milk boil).
Put the flour, sugar, yeast, egg and 1/ 2 tsp salt in a freestanding mixer with dough hook attachment. While the machine runs on a slow speed, pour in the warm milk and butter. Knead for 5 mins until the dough comes away from the sides of the bowl. Using floured hands, transfer to a lightly floured bowl, cover with cling film and leave in the fridge to prove overnight. (If you don’t have a free-standing mixer, mix the ingredients in a large bowl and knead the dough on a floured surface for 10 mins until smooth.)
To make the mayonnaise, put the egg yolk, mustard and some seasoning in a small bowl. Very slowly, drop by drop, gradually pour in the oil, whisking continuously so that the ingredients emulsify. If your mayonnaise begins to look a little thick, add a drop of water to loosen it. Add the vinegar, then season again to taste. Cover with cling film and put in the fridge. The mayonnaise and dough can be made the day before
The next day, briefly knead the dough on a floured surface to knock out the air. Divide the dough into 20 equal pieces and shape into balls. Put on a baking tray, cover loosely with cling film and leave to prove for 3-4 hrs in a warm place until doubled in size.
Next, prepare the crab. You need only the white leg and claw meat, but save the brown meat in the body of the crab for another time (see above). Use a sharp knife to crack open the claws and legs, and prise out all the white meat.
Line your work surface with cling film. Tip out the crabmeat and pick through it to check for shell fragments. If there is any shell, it should get stuck to the cling film.
Put the crabmeat in a small bowl, add the mayonnaise and lemon juice, then season to taste. Cover and put in the fridge until needed.
Heat the oil in a deep-fat fryer or large heavy-based saucepan to 180C or until a piece of bread browns in 20 secs. Working in batches, fry the doughnuts for 2-3 mins until cooked through and deep golden-brown. Drain them on kitchen paper.
When cool enough to handle, split the doughnuts nearly in half, leaving them attached at the base (this makes them easier to eat). Fill with the crab mixture and decorate with lemon zest and microherbs or cress. For further info about how to deep-fry safely see our guide.