Fit the dough hook to your mixer. Measure yeast into your mixer bowl and add milk to it. Leave the mixture for about 2 minutes to allow the yeast to dissolve. Stir if necessary.
Next, add the sifted flour, sugar, salt and egg into the yeast mixture and knead on the lowest speed for approximately 5 minutes until all the ingredients are well combined and the dough comes together.
Cut butter into small pieces and add into the dough. Continue mixing for another 6 to 7 minutes until butter is fully incorporated and the dough comes together smooth. At this point, the dough should be soft but not sticky to the fingers when pressed lightly.
Turn the mixer off. Turn the dough out onto clean work surface and form it into a ball. Place it in a large bowl. Make sure the bowl is large enough to allow the dough to triple in size without overflowing.
Cover the bowl with plastic wrap (cling wrap) and chill in the refrigerator between 8 to 12 hours (overnight).
Turn the proofed dough onto a floured workspace. Knead it for approximately 2 to 3 minutes until it becomes soft and pliable. If sticky, dust with a little flour and knead well until it is no longer sticky. Do not add too much flour. The kneading time at this stage is sufficient at 2 to 3 minutes.
Roll the dough to about 1 cm thick and cut out using a doughnut cutter. Alternatively, shape them into round balls, flatten and cut out a hole in the centers with a round cutter.
Place the cut donuts onto individually cut, flour-dusted parchment squares and arrange them on a large tray. Leave the dough to proof in a warm place until the doughnuts are about triple in size.
Add oil into a deep fryer or a deep pot. Heat it up until the oil reaches a temperature of between 173 to 175 ℃ (approximately 345 to 350 ℉).
Deep fry the donuts until they are golden brown. Turn them over halfway to allow both sides to cook. Remove the donuts from oil and drain them on a kitchen paper towel. Let them cool slightly before coating them with caster sugar.
To coat with sugar, add sugar into a small deep bowl. Dip each side of the donuts into the sugar until they are all well coated before serving.