In a medium bowl beat the egg yolks with the sugar until well blended. Add the sour cream, rum and vanilla then mix until smooth.
Sift together the flour, baking powder and salt then stir into the egg yolk mixture a little at a time. Turn the dough out onto a heavily floured surface and knead vigorously for about 1/2 hour. Allow the dough to absorb as much of the flour as it can so it is no longer sticky.
Separate dough into 4 or 5 portions and roll out very thin. The dough should be almost as thin as paper and slightly see-through.
Cut dough into strips about 3 1/2 cm wide and 10cm long. Make a 3 1/2 cm slit in the strip closer to one end. Pull the long end of the strip through the slit.
Heat the oil to 190 degrees C. Fry the biscuits quickly turning once. They should be golden but not brown.
Drain on paper towels and dust with icing sugar when cool.