Preheat oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a large bowl, cream together the butter and sugar until smooth. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour, baking powder, and salt; stir into the creamed mixture.
Roll dough into 1 inch balls and place them 2 inches apart on the prepared cookie sheets. Flatten the balls slightly.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Interesting Facts
Flying saucers originated in England in the 1950s.
The cookies are sometimes known as "spaceships" in the US.
The cookies are traditionally served during Halloween in the UK.