01 - Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
03 - In a large bowl, use an electric mixer to beat the softened butter and granulated sugar together until light and fluffy, about 2 to 3 minutes.
04 - Add the egg, egg yolk, and vanilla extract to the butter mixture. Beat until fully incorporated and smooth.
05 - With the mixer on low speed, alternately add the flour mixture and whole milk to the wet ingredients, beginning and ending with the flour. Mix until just combined and avoid overmixing.
06 - Transfer the dough to the prepared baking pan and spread it evenly. Use an offset spatula to smooth the top surface.
07 - Bake for 18 to 22 minutes, until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs. Do not overbake.
08 - Allow the bars to cool completely in the pan set on a wire rack before adding frosting.
09 - Beat the softened butter until creamy. Gradually add the sifted powdered sugar, milk, and vanilla extract, beating until the frosting is light and fluffy. Add food coloring if desired.
10 - Spread the frosting evenly over the cooled cookie bars. Top with sprinkles if using. Lift the bars out of the pan using the parchment overhang and cut into 16 squares. Serve and enjoy.