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, beat the softened butter and granulated sugar together using an electric mixer 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, 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. Smooth the surface with an offset spatula.
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 on a wire rack before frosting.
09 - Beat the softened butter until creamy. Gradually add the sifted powdered sugar, whole milk, and vanilla extract, beating until 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.