I found this on All4Women website, reproduced from Stuffed! a blog by Megan Deane. I havent made it, and would be interested to know how they turn out. Probably not a recipe for the beginner cook! I know, half an egg :(
Prep time does not allow for proving time (30 minutes)
Sift sugar, yeast and flour together, create a well in the middle
Place beer, milk, water and margarine in a pot and heat over medium heat until margarine is melted, take off the hot plate.
Whisk a whole egg but only use half the mixture
Pour the beer-milk-margarine mixture in the middle of the flour well, pour in half of the whisked egg mixture, and then the vanilla essence. Mix together really well.
Leave mixture, covered, in a warm place to prove for 30 minutes.
Knead dough and roll out into a "snake", pinch off bits and form small balls, maybe about the size of golfballs.
Heat the oil in a pot, fry the balls of dough slowly to ensure that they cook through. Once they are golden broan, remove carefully with a slotted spoon.
To make the syrup, place the 1/2 cup sugar and 1/2 cup water in a pot over a medium hot plate, keep stirring gently until the sugar has dissolved and the syrup thickens, pour the syrup over the doughnuts, decorate as desired.