Lightly oil 2 baking sheets. Place the flour, salt and butter in the mixing bowl. Fit the K-beater and mix on speed 1 to incorporate the butter into the flour. Mix in the sugar and yeast.

Replace the K-beater with the dough hook. Add the egg, lukewarm milk and about 90 ml (3 fl oz) lukewarm water and mix on minimum speed to form a soft dough.

Knead for 5-6 minutes on minimum speed, until the dough is smooth and elastic. Remove the mixing bowl, cover with lightly oiled clear film and leave to rise in a warm place for about 1 hour, or until doubled in size.

Using the dough hook on minimum speed for 30-60 seconds gently knead the dough to knock back. Transfer to a lightly floured surface and divide in half to make 8 ring and 8 jam doughnuts.

Cover half the dough. Roll the remaining dough to a thickness of about 1.25 cm (1/2 inch). Using a 7.5 cm (3 inch) plain cutter, cut out 8 rounds. Remove the centre with a 4 cm (1 1/2 inch) cutter to make 8 ring doughnuts.

Place on a prepared baking sheet and cover with oiled clear film. Divide the remaining dough into 8 and shape into round balls. Place on the other baking sheet and cover as before.

Leave the doughnuts in a warm place to rise for about 30 minutes, until doubled in size. Heat the oil for deep-frying to 180°C/350°F or until a cube of stale bread when added to the oil, turns golden brown in 30-60 seconds.

Cook the doughnuts, 3-4 at a time in the oil, for about 4-5 minutes, or until golden. Remove using a slotted spoon and transfer onto absorbent kitchen paper to drain.

Toss in caster sugar and set aside to cool. For the jam doughnuts, heat the jam with 5 ml (1 tsp) water in a small saucepan, until warm, stirring to combine. Cool and place in a piping bag fitted with a small plain nozzle.

Using a skewer make a small hole in the side of each round doughnut to insert the jam. Place the piping nozzle in the hole and squeeze a little jam into each doughnut.