Put all the ingredients for the doughnuts apart from the butter into the bowl and using an electric mixer with a dough hook attachment, mix on a medium speed for 8 minutes. The dough needs to start coming away from the sides and forming a ball.
Turn off the mixer and let the dough rest for 1 minute.
Start the mixer up again on a medium speed and slowly add the butter to the dough – about 25g at a time. Once it is all incorporated (and be patient as it may take a little while), mix on high speed for 5 minutes, until the dough is glossy, smooth and very elastic when pulled. Cover the bowl with clingfilm and leave to prove until it has doubled in size.
Once it’s ballooned a little, knock back the dough, then re-cover the bowl and put into the fridge to chill overnight.
The next day, take the dough out of the fridge and cut it into 50g pieces (you should get about 20). Roll them into smooth, taut, tight buns and place them on a floured baking tray, leaving plenty of room between them as you don’t want them to stick together while they prove. Cover lightly with clingfilm and leave for about 4 hours, or until about doubled in size.
Fill a heavy-based saucepan with sunflower oil (or use a deep-fat fryer if you have one!). Heat the oil to 180C. Be careful as hot oil is dangerous.
hen the oil is heated to the correct temperature, carefully remove the doughnuts from the tray by sliding a floured pastry scraper underneath them. Be careful not to deflate and knock all the air out of them. Gently place in the oil, doing two or three at a time depending on the size of your pan. Fry for 2 minutes on each side until golden brown. They should puff up and float, so you may need to gently push them down after about a minute to help them colour evenly.
Remove from the fryer and place on kitchen paper to drain, then toss them in a bowl of caster sugar while still warm. Repeat until all are fried, but make sure the oil temperature is correct every time before you fry. Set aside to cool before filling.