In a large bowl add yeast to flour and mix well. Next mix in the caster sugar and vanilla sugar. Make a well in the centre and add eggs and milkl. Now mix well with your hands until a dough is formed (do it by hand, it's actually easier!).
Cover bowl with a clean towel and let rise for 2 hours.
Roll out dough on a floured work surface with a rolling pin and cut out shapes of your choice.
Heat oil in a large frying pan or deep fryer and fry beignets in oil till browned. Degrease on kitchen paper, sprinkle with icing sugar and serve.
Change oil occasionally while frying as it will get cloudy with flour. Also, take care not to burn the oil as it will give the beignets a bad flavour.