Preheat oven to 325 degrees F. Line a cookie sheet with parchment paper or a Silpat mat.
In a saucepan over medium heat, melt the butter until it starts to brown. When the butter has browned and is ready, the foam will have subsided and it will have turned a nutty color.
Pour the browned butter into a medium bowl and stir in the brown sugar and vanilla. In a small bowl, whisk the flour and baking powder together. With a spoon, stir the flour mixture into the butter mixture until combined and uniform in color.
Drop dough by tablespoonful onto the cookie sheet.
Bake for 12 minutes.