Preheat the oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar together on medium speed until light and fluffy, about 3 minutes.
Add the egg and 2 teaspoons vanilla extract to the butter mixture and beat until combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Press the cookie dough evenly into the prepared baking pan, smoothing the top with a spatula.
Bake for 22-25 minutes, or until the edges are lightly golden and a toothpick inserted in the center comes out clean.
Remove the pan from the oven and allow the cookie bars to cool completely in the pan on a wire rack.
While the bars are cooling, prepare the icing by whisking together the powdered sugar, milk, and 1/2 teaspoon vanilla extract in a small bowl until smooth.
Once the cookie bars are cooled, spread the icing evenly over the top.
Immediately sprinkle the red sanding sugar on one third of the bars, the white nonpareils on the middle third, and the blue sanding sugar on the remaining third to create a patriotic look.
Allow the icing to set for at least 30 minutes before slicing into 16 bars and serving.