Gently warm the milk (it needs to be lukewarm, too hot will kill the yeast). Dissolve the yeast in the milk. Add the melted butter, sugar, salt and eggs to the mixture. Gently work in the flour until you have a smooth dough, then leave to rise for 30 minutes.
While the dough is rising, make the filling. Whisk together the eggs and sugar then whisk in the milk and cornflour. Cook over a gentle heat until the mixture boils and thickens. Add the vanilla to flavour and leave to cool.
Cover 2 large baking trays in baking paper and heat the oven to 225 degrees C.
Divide the dough into two and roll the first piece into a 30x30cm square. Cut this into 9 10x10cm squares. Put one teaspoon of the filling in the middle of each square. Fold one corner over the mixture, then its opposite corner. Then fold the remaining corners over.
Place each bun on the baking tray with the folded side face down. Brush each bun with egg and bake for 15 minutes. Let the buns cool. Mix all the ingredients for the icing together and spread onto each bun.
Mix all the ingredients for the icing together and spread onto each bun.