Sift the flours into a mixing bowl with the yeast and salt.  Make a well in the centre, then add the butter, sugar, milk and egg.  Gradually bring the ingredients together, add the water a little at a time until you have a soft, quite wet dough.

Lightly dust the worktop with flour, then turn the dough out and knead well for 10 minutes until smooth and elastic. 

Transfer to a lightly oiled bowl and cover with a tea towel, then leave in a warm place for an hour or until the dough has doubled in size.

Knock back the dough, divide into 12 even pieces, then shape into finger buns.  Arrange on a lined baking tray in two rows of 6 so the buns are almost touching.

Cover the buns with cling film, then leave in a warm place for 50 minutes to double in size. 

Preheat the oven to 180 fan

Bake in the oven for 15 minutes until risen and golden, then transfer to a wire rack to cool.

Meanwhile, mix the icing sugar and water or lemon juice together to form a thick but runny icing.  Dip each bun into icing upside down.  Leave for a minute or so to set.