Put the butter in a bowl and add the sugar, little by little, beating until the mixture is creamy.
Blend in the egg and beat until light. Mix the flour and baking powder and blend along with the vanilla into the creamed mixture until a stiff dough forms.
Knead lightly and divide into 2 parts. Roll each part to make a 2-inch diameter log. Wrap in waxed paper and foil and chill at least 1 hour or up to 2 weeks.
Cover baking sheets with parchment paper or lightly grease them.
Preheat oven to 375°F Cut dough into 1/4 inch thick slices. Place on baking sheet about 2 inches apart. Bake for 10 to 12 minutes until golden. Allow to cool on the baking sheets, then dust with powdered sugar. Store in an airtight container. Makes 3 dozen cookies.