Heat oil in deep-fryer or large heavy skillet to 375 degrees F (190 degrees C).
In a large bowl, whisk together eggs, vanilla and melted butter until well blended.
Mix in the salt and baking powder. Gradually stir in flour with a wooden spoon until dough is stiff. Turn out onto a floured surface and knead in as much flour as necessary to make a smooth stiff dough. Dough should not be sticky.
Roll the dough out paper thin and cut into 3 inch squares.
Fry in the hot oil, turning once until golden.
Drain in colander and place them into a waxed paper lined bushel basket. Dust with confectioners' sugar when cool.
