Blend flour and confectioners' sugar; chill.
Add potato and mix gently with a fork.
Cut in butter until pieces are the size of small peas.
Sprinkle extract over mixture, a few drops at a time, mixing lightly with fork (dough should be crumbly).
Shape dough into a ball; chill thoroughly.
Roll dough, a half at a time.
1/4 inch thick on a floured surface; cut with 13/4 inch round cutter and cut centers from half the rounds with a 3/4 inch round cutter.
Place rounds, rings, and centers on separate ungreased cookie sheets.
Bake at 400°F 10 to 15 minutes.
When cool, spread rounds with currant jelly and top with rings; fill centers of rings with a small amount of jelly; top with centers.