Preheat oven to 350˚F. Line a baking sheet with parchment paper or silicone baking sheet.
In a medium bowl, cream together the peanut butter and butter until smooth. Add the brown sugar, and beat until fully combined. Add in the egg and vanilla, and continue beating until creamy.
In a separate bowl, mix together the flour and baking powder. Gradually add the dry ingredients to the wet ingredients, and mix until fully incorporated.
Place the white sugar in a bowl. Roll spoonfuls of cookie dough into balls, and roll balls in sugar to coat them completely.
Place the cookie balls 2 inches apart on a prepared baking sheet.
Bake in the preheated oven for about 12 minutes, or until cookies are just brown around the edges. Remove from oven and let the cookies cool at least 10 minutes on baking sheet before transferring cookies to rack to cool completely.