Sift the flour, yeast, sugar and salt into a large bowl. Add the egg and mix well, pour in the milk and mix into a smooth batter.
Stir in the currants and vanilla. Cover the bowl, and leave the batter in a warm place to rise until double in size (around 2 hours).
Heat the oil in a deep-fryer, or heavy deep pan to 190 °C.
Use 2 metal spoons to shape scoops of dough into balls, and drop them carefully into the hot oil.
Fry the balls until golden brown, about 8 minutes. The doughnuts should be soft and not greasy.
If the oil is not hot enough, the outside will be tough and the insides greasy. Drain finished doughnuts on paper towels and dust with confectioners' sugar.
Serve them piled on a dish with more confectioners' sugar dusted over them. Eat them hot.