Preheat oven to 350 degrees. Line a cookie sheet with parchment paper.
In a large bowl beat butter until creamy. Add sugar, baking powder and salt. Mix well. Add egg and vanilla. Beat in the flour. Cover and chill dough until easy to handle.
Use one teaspoon of dough and shape into a ball. Place 1 inch apart on cookie sheet. Using a flour the bottom of a drinking glass. Flatten into 1 1/2 inch rounds.
Bake 10 to 12 minutes or until edges are golden. Cool on a cookie sheet.