Preheat oven to 350 degrees F. Spray a 9x13-inch baking pan lightly with nonstick cooking spray. Cut a piece of parchment paper large enough to cover the bottom of the pan and overhang the sides. About 17-inches long and 9-inches wide.
Mix together the butter, sugar, eggs, and vanilla extract until smooth, about one minute on medium speed. Add the eggs, one at a time, and allow them to incorporate after each addition. After you add the second egg, mix for one minute.
Stop the mixer and scrape down the bottom and sides of the bowl with a rubber spatula. Mix for 20 seconds.
Stop the mixer and add the flour, baking powder, and salt. Mix until a dough forms.
Press the dough evenly into the prepared pan. (If the dough sticks to your hands, dust them lightly with gluten-free flour.)
Bake until the edges of the bars are golden brown, about 20 minutes.
Remove the pan from the oven and allow the bars to cool in the pan. Lift the bars out of the pan using the overhanging parchment paper.
Frost the top of the bars. (recipe below) Sprinkle with colored sugar or gluten-free sprinkles. Cut into 15 bars. Store wrapped bars on the counter for up to four days.
For the Frosting
Mix together the butter and powdered sugar until smooth. Add the milk and vanilla. Mix until fluffy. If frosting seems too thick, add additional milk, one teaspoon at a time. Spread on cooled bars.