In a jug, mix the water, milk, yeast and honey. Leave it for five minutes or so. the mixture should start to bubble and look foamy.
In a mixer, beat the flours, butter and salt together until the butter is combined and there are no lumps
Now slowly pour in the yeast mixture and add one egg. Beat with the mixer for another 10 minutes. The dough will be sticky - don't worry, it's supposed to be.
Lightly oil a large bowl and place the dough inside, using a spatula to get as much as you can out of the mixer and off the beater attatchment. Cover with some cling film and leave for 2 hours.
When the dough has doubled in size, remove from the bowl and place on a floured surface. Punch the dough to knock out the air. Now cut into 8 pieces of around the same size.
To shape the buns, place one on the surface and gently pull the edges into the middle. Turn it over and tuck under so the smooth side is on top. Repeat with the other rolls.
Place all the rolls onto a baking tray that is covered with a sheet of baking paper, and put the tray in a large carrier bag (I actually use a fresh bin bag, just to ensure it is roomy enough to not touch any of the dough - it works!) Leave to prove for another 2 hours.
Once the buns have risen again, set the oven to 200°C. Beat the second egg with 1 tsp milk, and then brush over the tops and sides of the buns.
I like to add some sesame seeds to the top to give it the classix burger bun look, but htis is optional. Place in the oven for 15 minutes until they are a beautiful golden brown. Done!