1.Combine yeast and the water in a small bowl, stir until yeast is dissolved.
2.Place butter and milk in a small saucepan over high heat; stir until butter is melted. Cool until lukewarm.
3.Place yeast mixture, butter mixture, sugar, salt, egg yolks and sifted flour in a large bowl; beat with a wooden spoon until mixture forms a soft sticky dough. Cover bowl; stand in a warm place for about 1 hour or until dough has doubled in size.
4.Turn dough onto a lightly floured surface; knead gently until just smooth. Roll dough out until 1cm thick. Using a floured 8cm round cutter and a floured 2.5cm round cutter, cut rounds from dough, removing the centres with the smaller cutter. Repeat with remaining dough, re-rolling when necessary. Place rounds on baking-paper-lined oven trays. Stand for 15 minutes.
5.Heat oil in a large saucepan or wok until it reaches 150°C on a candy thermometer (or until the base of a wooden spoon bubbles when placed in the oil). Deep-fry doughnuts three at a time for 2 minutes each side or until golden brown. Drain on paper towel.
6.Toss doughnuts immediately in combined extra sugar and cinnamon; serve doughnuts warm.
Never walk away from hot oil; if doughnuts are over browning, reduce the heat of the oil. They are best eaten on the day of making. Reheat cold doughnuts in 10-second bursts in the microwave until just warm.