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, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until combined.
Gradually add the dry ingredients to the wet ingredients, alternating with the 1/4 cup of whole milk, beginning and ending with the dry ingredients. Mix until just combined.
Spread 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 from the oven and let the cookie bars cool completely in the pan on a wire rack.
While the bars cool, prepare the frosting. In a medium bowl, beat the powdered sugar, 2 tablespoons softened butter, 1 tablespoon milk, and 1/2 teaspoon vanilla extract until smooth and creamy.
Divide the frosting into three small bowls. Leave one bowl white, add a few drops of red gel food coloring to the second bowl and mix until evenly colored, and add a few drops of blue gel food coloring to the third bowl and mix well.
Once the cookie bars are completely cooled, spread the white frosting evenly over the top.
Use the red and blue frostings to create stripes or stars on top of the white frosting. Decorate with red, white, and blue sanding sugars and white nonpareils to enhance the patriotic look.
Allow the frosting to set for about 30 minutes before cutting into 16 bars and serving.