Adjust oven rack to the middle position and preheat the oven to 350 degrees.
Spray a 13- by 9-inch baking pan with cooking spray or grease with butter.
In a medium bowl, whisk the flour, baking powder and salt together. Set aside.
In a second medium bowl, whisk the melted butter and brown sugar together until combined. Add the eggs and vanilla and mix well. Using a rubber spatula, fold the dry ingredients into the egg mixture until just combined.
Spoon the batter into the prepared pan, smoothing the top with a rubber spatula.
Bake until the top is shiny and cracked and feels firm to the touch, for 22 to 25 minutes.
Place the pan on a rack and let cool completely (about an hour). Cut into 1 1/2- by 2-inch bars.