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To make the gnocchi, cook the potatoes in boiling water for 40-50 mins until very tender, then drain well. Peel away the skin and press through a sieve or a potato ricer into a bowl.
While the potatoes are still warm, add 1 tsp salt, the butter, egg and half the flour. Lightly mix together and turn out onto a floured board. Gradually knead in enough of the remaining flour to make a smooth, soft but slightly sticky dough.
Roll out the dough into sausages, 2.5cm in diameter. Cut into roughly 2cm pieces and put on a floured tea towel to prevent the gnocchi sticking together.
Bring a large pan of water to the boil. Drop the gnocchi into the water in batches and allow to cook for 2-3 mins until they float to the surface. Remove with a slotted spoon and keep hot while you cook the rest.
Meanwhile, gently heat the butter in a large heavy-based pan, add the shallots and garlic, and gently soften for 5-6 mins. Add the samphire and cook for 4-6 mins more.
Add the gnocchi to the pan with most of the parsley. Gently toss everything together and season. Serve immediately, scattered with the rest of the parsley.