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Put the flour, yeast, sugar and ½ tsp salt into a large bowl, mix, then make a well in the middle.
Beat the egg yolks, milk and melted butter together, tip into the well, then bring together with a knife or pastry scraper. The dough will seem wet and rough. Leave to stand for 10 minutes and it should firm up a little.
Oil the work surface and your hands, then tip out the dough and knead for about 5 minutes until it looks smoother and feels springy. Keep oiling your hands if the dough sticks. Let it rise in an oiled, covered bowl in a warm place for about 2 hours or until doubled in size.
Give the dough another quick knead (knock back), then shape into walnut-size balls and place on lined baking sheets, well spaced. Cover again, then leave to rise for an hour and the dough no longer springs back when you prod it.
Heat oven to 190C.
Bake for 12-15 minutes until risen and dark golden. Melt 50g butter in a pan and put 50g sugar into a large bowl. Let the doughnuts cool for a few minutes, then brush with butter and roll in sugar.
Spoon jam into a piping bag with a 5mm nozzle. Poke a hole in each doughnut, then push in the nozzle and squeeze in a little jam. Best served warm.
To make the dough, place all ingredients into a large bowl keeping back a quarter of the water.
Stir with your hands until a dough is formed.
Slowly add the remaining water and knead the dough in the bowl for about four minutes. (Alternatively, you could bung it all in the mixer fitted with a dough hook and mix for 10 minutes).
Tip dough onto a lightly floured surface and knead well for 10 minutes, until the dough is smooth and elastic.
Place the dough into a clean bowl, cover with a damp tea towel and leave to rise for an hour.
Tip the dough out onto a very lightly floured surface, and knock it back by kneading it a few times.
Divide the dough into 10 equal portions and shape each portion into a ball.
Place all balls onto a floured baking tray and allow to rise for an hour.
Heat a deep fat fryer, filled with oil, to 180C.
Lower each doughnut into the fryer carefully, cook each side for about five minutes or until golden brown. Remove the doughnuts from the oil with a slotted spoon and immediately roll in caster sugar so that the hot fat makes the sugar stick to the sides.
Set aside and leave to cool.
When completely cool, using a small, sharp, knife make a cut into the side of the doughnut, reaching to the centre.
Spoon some smooth or sieved strawberry jam into a piping bag and pipe the jam inside.
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