Tip the eggs and 60ml water into the bowl of a stand mixer, then mix in the flour using a dough hook attachment. Beat on low for 2 mins until combined. Cover and leave to rest for 10-15 mins, then knead with the dough hook for 2 mins more, or until smooth and elastic. Cover and leave to rest for 30 mins.

Meanwhile, for the filling, heat 1 tbsp oil in a frying pan over a medium-low heat and cook the onions for 12-15 mins until softened and translucent. Tip in the sauerkraut and cook for 5 mins, stirring in a splash of water if it starts to stick. Transfer to a bowl. Heat the remaining oil in the pan over a medium-high heat and cook the mushrooms for 5-7 mins until browned all over. Add to the onion mixture along with the chestnuts. Season well and leave to cool.

While the filling cools, prepare the shallots. Heat the oil in a saucepan over a medium-high heat. Add a small piece of shallot to check the oil is hot enough – if it sizzles, it’s ready. Toss the shallots with the flour, then fry in batches until golden. Transfer to a plate lined with kitchen paper using a slotted spoon, and sprinkle over some salt.

Dust two large baking trays with semolina or flour. Divide the dough into two and roll one piece out until it’s about 3-4mm thick, keeping the remaining dough wrapped in a tea towel to prevent it drying out. Stamp out 8-10cm circles using a pastry cutter. Fill each with a scant tablespoon of the filling, then bring the edges together. Making sure there is no air trapped inside the dumpling, pinch the edges together to seal, forming a half-moon shape. You can then crimp the edges if you wish. Arrange on the baking tray as you go. Repeat, rolling out the second piece of dough, until you’ve used all the dough and filling.

Cook the dumplings in a large pan of boiling salted water for 3-4 mins, or until they rise to the surface. Spoon crème fraîche over the serving plates, then top with the dumplings and crispy shallots.