Heat together the water, butter and milk until the butter has melted.
In a separate bowl (or the bowl of a stand mixer), mix together the flour, caster sugar, salt and yeast.
Pour the warm butter mixture into the flour and add the egg.
Stir to combine and knead for 5-8 minutes until the dough is smooth and soft. If the dough is sticky, add a little more flour.
Place in a clean bowl and cover with a damp tea towel. Allow to rise for 1 hour
Roll out the dough and cut out the doughnuts to your preference. Place on a floured surface and cover with a damp tea towel and allow to rise for another hour.
In the meantime, make the glaze. Combine all the ingredients in the bowl of a food processor and blend until smooth. Place in a jug and press a piece of cling wrap to the surface. This will prevent the glaze from forming a skin.
Heat the oil in a large pot. Carefully add 2-3 doughnuts to the hot oil at a time. Immediately flip the doughnuts when they are in the oil. This will allow them to rise more. Fry until the doughnuts are cooked through and golden brown on both sides.
Remove from the oil and drain on kitchen paper before pouring over the glaze.