1. Place the flour, sugar, yeast, eggs and salt with 75ml water in the bowl of an electric stand mixer fitted with the dough hook. Beat on a medium speed until the dough starts to come away from the sides, 7–8 minutes.
Add half of the butter and when well incorporated, add the rest. Beat on a high speed for 5-6 minutes, until smooth, glossy and elastic. Cover the bowl with clingfilm and leave in a warm place to rise, until doubled in size – about 1 hour.
Turn the dough out onto a lightly floured surface and knead a little to remove excess air. Divide the mixture into 18 x 25g balls. They will seem small, but will expand with a second prove and when fried.
Roll into small, tight balls and place on a lightly floured baking tray, leaving plenty of space between each one. Prove in a warm place for 2-3 hours, until doubled in size.
Heat the oil in a deep fat fryer or large, deep frying pan. If you can, monitor the heat of the oil so that it is around 180°C. Deep- fry each doughnut for about 11⁄2 minutes on each side.
Remove with a slotted spoon onto kitchen paper and then immediately roll in the caster sugar. Repeat with all the doughnuts.
Mash the raspberries into the vanilla yogurt and transfer to a piping bag fitted with a medium round nozzle. When the doughnuts are cool, use a knife to cut a deep incision in each. Pipe in the yogurt mix and then serve as soon as possible.