Cream butter and sugar well. Beat the egg and add to the creamed mixture, along with the vanilla extract. Gradually add the flour. Drop the dough by the teaspoon, about an inch apart onto ungreased baking sheets (or lined with baking parchment). Bake at 350 degrees for about 15 minutes or until lightly browned around the edges. Let cookies rest on the baking sheet briefly, then remove to a cooling rack to cool completely. Store in a covered container.