Preheat your oven to 350°F and line two cookie sheets with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt.
In a separate bowl, cream together the butter and sugar until fluffy, then mix in the egg and vanilla.
Gradually add the dry ingredients to the wet ingredients, mixing until combined.
Roll the dough into balls, coat them in sugar, then flatten slightly on the baking sheets.
Bake for 9-10 minutes, then cool on a wire rack.