Preheat oven to 350 degrees F (175 degrees C).
In a large bowl, cream together the 1/2 cup room-temperature butter and 1 cup sugar until light and fluffy; add 1 egg and 1 tablespoon vanilla extract, mixing thoroughly.
In a separate bowl, combine 1 ⅓ cups flour, ¾ teaspoon baking powder, and ¼ teaspoon salt. Then fold the flour mixture into the butter mixture, just until blended
Use a small cookie scoop or drop cookies approximately 1 tablespoon at a time about 2 inches apart onto ungreased baking sheets. (I needed two baking sheets for this recipe!)
Bake in the preheated oven until edges of cookies are golden brown, 13 to 15 minutes. Cool cookies on wire racks.
NOTE: Using my 1 Tablespoon cookie scoop netted 36 approximately 2" cookies from this recipe. You can use a smaller 1 teaspoon cookie scoop to get more numerous yet smaller vanilla wafer cookies.