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 flour, baking powder, and salt. Set aside.
03 - In a large bowl, 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.
05 - On low speed, alternately add the flour mixture and milk, beginning and ending with the flour. Mix until just combined; do not overmix.
06 - Spread the dough evenly into the prepared pan and smooth the top 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 - Cool the bars completely in the pan on a wire rack.
09 - Beat the softened butter until creamy. Gradually add powdered sugar, milk, and vanilla, beating until light and fluffy. Tint with 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.