Sift the strong white flour and the salt into a large bowl. Add the chilled cubed butter and, using your fingertips, rub it in until the mixture resembles breadcrumbs.
Heat the milk in a saucepan until it is warm, then stir in the caster sugar and the dried yeast, fresh yeast or fast-acting yeast, whichever you're using. Remove the saucepan from the heat and allow it to stand for 5 minutes until the yeast goes frothy. If you're using fast-acting yeast, there is no need to let the mixture stand. Using a whisk, mix in the egg yolks.
Pour most of this liquid into the flour-and-butter mixture and mix to a soft but not a wet dough - you may not need all of the liquid. Knead the dough, either by hand or in an electric food mixer using the dough hook, for approximately 5 minutes or until the mixture is smooth and slightly springy.
Place the dough in an oiled bowl and coat the dough with oil by rolling it around the bowl. Cover the bowl with cling film or a clean tea towel and leave it in a warm place for about 1 hour or until the dough has doubled in size.
Knock back the risen dough and knead it for 2-3 minutes. Roll it out on a floured work surface to 1cm (½in) thick, then, using a 5cm (2in) plain cutter, cut out about 24 rounds.
Into the centre of each round, insert your forefinger until it goes all the way down through the dough. With your forefinger, lift up the doughnut and swing it around in the air! This will make the hole wider.
Place the doughnuts on an oiled baking tray and tidy each one up into a round. Cover again with oiled cling film or a tea towel and leave in a warm place for approximately 30-45 minutes until the doughnuts have nearly doubled in size.
Meanwhile, heat the vegetable oil in a deep fryer to a temperature of 180-190°C (350-375°F). I normally use a wide saucepan filled with about 5-6cm/2-2 ½in of vegetable oil. You can check the temperature with a sugar thermometer or using a 1cm (½in) cube of bread, which should sizzle and turn nicely golden brown in about 30-40 seconds.
Carefully place the doughnuts in the oil with a slotted spoon and cook for 2-3 minutes on each side until golden brown. Remove from the oil with the slotted spoon and toss immediately in the caster sugar to serve.
See Rachel's Churros con Chocolate Recipe