Place the flours, water, milk, yeast, salt, sugar and lemon zest into a large bowl and mix with a fork until combined. Add the beaten egg and butter and continue to mix until the mixture comes together as a sticky dough.
Tip the dough onto a lightly floured work surface and knead for five minutes, or until the dough is smooth and elastic.
Lightly oil a bowl with a little of the vegetable oil.
Place the dough into the bowl and turn until it is covered in the oil. Cover the bowl with cling film and set aside in a warm place for one hour, or until the dough has doubled in size.
Lightly grease two baking trays.
Knock the dough back to its original size and turn it out onto a lightly floured work surface. Divide the dough into eight portions, shape them into rounds and place onto the baking trays. Ensure the rolls are well spaced. Cover with a tea towel and set aside to prove for 30 minutes.
Preheat the oven to 220C/425F/Gas 7.
Bake the buns in the oven for 20-25 minutes or until well risen and golden-brown. Remove the buns from the oven and set aside to cool on a wire rack.
Meanwhile for the icing, mix the icing sugar and lemon juice together in a bowl until smooth.
Once the buns have completely cooled, spread the icing on top of them and set aside until the icing has hardened.