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Tip the yeast and 1 tbsp sugar into a large bowl, and pour over 100ml warm water. Leave for 10 mins until the mixture becomes frothy.
Pour 200ml warm water into the bowl, then stir in the salt and half the flour. Keep adding the remaining flour (you may not have to use it all) and mixing with your hands until you have a soft but not sticky dough. Then knead for 10 mins until the dough feels smooth and elastic. Shape into a ball and put in a clean, lightly oiled bowl. Cover loosely and leave in a warm place until doubled in size, about 1hr.
Heat the oven to 220C/200C fan/gas 7. On a lightly floured surface, divide the dough into 10 pieces, each about 85g. Shape each piece into a flattish ball, then take a wooden spoon and use the handle to make a hole in the middle of each ball. Slip the spoon into the hole, then twirl the bagel around the spoon to make a hole about 3cm wide. Cover the bagel loosely while you shape the remaining dough.
Meanwhile, bring a large pan of water to the boil and tip in the remaining sugar. Slip the bagels into the boiling water – no more than four at a time. Cook for 1-2 mins, turning over in the water until the bagels have puffed slightly and a skin has formed. Remove with a slotted spoon and drain away any excess water. Sprinkle over your choice of topping and place on a baking tray lined with parchment. Bake in the oven for 25 mins until browned and crisp – the bases should sound hollow when tapped. Leave to cool on a wire rack, then serve with your favourite filling.