Cream the butter and sugar in a medium size mixing bowl. Mix flour, baking powder, salt, egg and vanilla extract into the butter-sugar mixture. Cool dough in the refrigerator for 1 hour.
On a lightly floured surface roll dough out to 1/4 inch thick. Cut the dough into rounds with a round cookie cutter or glass. Using the tip of a teaspoon place a small drop of apricot preserves into the middle of the circle. Brush edges with water and fold the dough over so that the cookie is in the shape of a half moon; seal edges Arrange on ungreased cookie sheets.
Bake for 8 to 12 minutes, or until golden brown. Dust the cookies with powdered sugar while still hot.