Combine the flour, yeast, salt and sugar in a large bowl and mix well. Put the butter into a bowl with the warm milk and water, and stir to melt. Pour this into the mixing bowl, along with the egg, and stir until it comes together into a dough: it should be firm, but soft.

Tip on to a lightly floured surface, or into a mixer fitted with a dough hook, and knead until smooth and elastic (about 10 minutes). Put into a lightly greased bowl, cover with a damp tea towel, and leave in a warm place until doubled in size (about an hour).

Shape into 6 balls of about 80g each, folding each side tightly into the centre in turn, turning as you go, then turn the ball over and put it on a lightly floured baking tray or board, spacing them well apart. Cover and leave to rise again for 45 minutes.

Heat the oil in a large pan or deep-fat fryer to 160C. Cook the doughnuts in 2 batches for about 3 minutes on each side, until golden, then blot with kitchen paper and sprinkle with caster sugar. Allow to cool slightly, then make a small hole in the side of each, and use a piping bag to inject a splodge of jam. Eat immediately, while they're still warm.