Place the water (lukewarm) in a cup and add the yeast and a pinch of sugar. Set aside for 5 minutes until the yeast starts to foam.
Add the flour, salt and sugar to the bowl of a stand mixer. Add the yeast mixture, along with the butter, milk, egg and vinegar. Mix until a dough forms and then knead for about 5 minutes. Cover and set aside for an hour, until doubled in size.
Place the dough on a floured surface and knead lightly. Roll the dough out to a thickness of about 1/2". Use a 1" round cutter to cut out balls of dough.
Place each ball onto a tray lined with baking paper. Repeat until all the dough is used.
Place the tray into the oven, along with a container of boiling water. Leave for another 30 minutes to rise.
Heat enough oil in a saucepan to be able to deep fry the donuts. Heat the oil to 180 °C.
Drop the donuts into the oil, 1 or 2 at a time. As soon as the turn golden, turn them over. Remove once both sides are cooked. Transfer to a plate lined with paper towel while you cook the remaining donuts.
When cooled, roll each donut in sugar to coat evenly.