Preheat oven to 375F (190C).
In a small bowl, combine the flour and baking powder with a whisk.
In another bowl, cream the butter and add sugar gradually. Beat the eggs until light and add to the butter-sugar mixture, beating well. Add the vanilla extract. Add the flour and baking powder mixture slowly, blending to make a soft and malleable dough.
To shape each ring, pull off a piece of dough the size of a walnut and roll it out by hand into a rope about 4 inches long. Form a circle with it, and place on an ungreased cookie sheet, leaving some distance between the cookies. Brush the tops lightly with beaten egg and bake for 20 minutes or until golden brown.
Cool on racks.
Yield: 4-5 dozen