Beat brown sugar, butter, eggs, and vanilla extract together in a bowl using an electric mixer until smooth and creamy.
Whisk flour, baking powder, and salt together in a separate bowl. Stir flour mixture into butter mixture until dough is fully combined.
Pour confectioners' sugar onto a large plate. Spoon dough, 1 1/2 teaspoons per cookie, onto confectioners' sugar and roll to coat. Arrange coated dough on a baking sheet.
Bake in the preheated oven until edges are lightly browned, 12 to 14 minutes. Cool cookies on baking pan for 2 minutes before transferring to a wire rack to cool completely.
