Combine flour, yeast, sugar and salt in a large mixing bowl, set aside. In a microwave safe bowl, add the milk and butter, microwave on HIGH in 15 second increments until very warm, but not hot to the touch (120° to 130°F, butter does not need to be completely melted). Add the milk mixture and beaten egg into the dry ingredients, mix thoroughly with a wooden spoon.
Knead onto a lightly floured surface for 10 minutes (or use the dough hook attachment on your mixer). Transfer dough to a lightly greased mixing bowl, cover the bowl with a clean tea towel and leave to rise until doubled in size – up to 2 hours depending on how warm your kitchen is.
To make the filling by combine sugar, corn starch and salt in a medium saucepan. Gradually stir in milk until smooth. Add egg yolks. Stirring constantly, bring to boil over medium heat and boil 1 minute. Stir in vanilla.
Once doubled in size, turn dough out onto floured surface, gently knead 5 times to get air out. Shape dough into a flat disc and cut into 12 even pieces (use a weigh scale if you like). Individually knead each piece of dough, pinching sides together to create a smooth ball. Place rough side down on lightly greased baking sheet, evenly spaced for room to grow.
Cover the dough balls with a clean tea towel and leave to proof until almost doubled in size. Preheat your oven to 375°F, place a roasting pan full of boiling water on the base of your oven.
Once doubled in size, uncover and bake the doughnuts for 12-15 minutes until golden brown. Remove from oven, let the doughnuts cool for a few minutes then brush with the melted butter and roll in sugar. Fill a piping bag with custard, poke a hole in each doughnut with a skewer, then squeeze custard into the hole.
Best served warm.
Tip : You can make you own castor sugar by blending regular white sugar in your blender!