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 whole egg, egg yolk, and pure vanilla extract to the butter mixture. Beat until fully incorporated and smooth.
05 - On low speed, alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour. Mix until just combined without overmixing.
06 - Transfer the dough to the prepared baking pan and spread it evenly. Smooth the surface using an offset spatula.
07 - Bake for 18 to 22 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs. Avoid overbaking.
08 - Let the bars cool completely in the pan set on a wire rack before adding frosting.
09 - Beat the softened butter until creamy. Gradually add sifted powdered sugar, whole milk, and pure vanilla extract, beating until light and fluffy. Add food coloring if desired.
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 and enjoy.