01 - Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper, leaving an overhang on two 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 with an electric mixer until pale, light, and fluffy, about 2 to 3 minutes.
04 - Add the whole egg, egg yolk, and vanilla extract to the butter mixture. Beat on medium speed until fully incorporated and smooth.
05 - With the mixer on low speed, alternately add the flour mixture and whole milk to the batter, beginning and ending with the flour. Mix until just combined and stop to avoid overmixing.
06 - Transfer the dough to the prepared baking pan and spread it evenly using an offset spatula, smoothing the surface.
07 - Bake for 18 to 22 minutes until the edges are lightly golden and a toothpick inserted in the center comes out with a few moist crumbs. Do not overbake.
08 - Allow the bars to cool completely in the pan set on a wire rack before frosting.
09 - Beat the softened butter until creamy using an electric mixer. Gradually add sifted powdered sugar, whole milk, and vanilla extract, beating until the frosting is light and fluffy. Add food coloring if desired and mix until evenly tinted.
10 - Spread the frosting evenly over the cooled bars. Top with sprinkles if using. Lift the bars out of the pan using the parchment overhang and cut into 16 squares. Serve.