Preheat oven to 350°F.
Line a baking sheet with parchment paper.
Add butter to a small saucepan and cook over medium-low heat until butter begins to melt. Continue to cook butter until it has turned an amber color and smells toasty but not burnt. The butter will darken quickly once it begins to turn golden, so watch carefully.
Pour butter from the saucepan into a small bowl, scraping the browned bits from the bottom of the pan with a spatula. Allow to cool for 10 - 15 minutes.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, whisk together the sugar, egg, and vanilla extract. Add the cooled butter. Stir in flour mixture, mixing only until no streaks of flour remain.
Drop 1-inch balls onto prepared baking sheet. Bake for 10 - 12 minutes, until the edges are set and just start to brown.
Cool cookies on a wire rack.