Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper. Leave some paper hanging on the sides, it can help you to remove bars from the pan. Set aside.
In a large mixing bowl, beat softened butter and sugar using an electric mixer until well combined and smooth. Beat in the egg, egg yolk, and vanilla extract. Don’t forget to scrape the bottom and the sides of the bowl with a spatula to make sure all ingredients are well combined.
In a separate bowl, combine the flour, cornstarch, salt, baking powder, and baking soda. Add to the wet ingredients. Beat on low speed until just combined and no lumps of flour remain. Fold in the rainbow sprinkles using a rubber spatula.
Transfer the dough to the prepared baking pan. Spread evenly. Bake in the preheated oven for 22-26 minutes or until the edges are slightly browned and the center is golden and slightly gooey. Remove the baking pan from the oven and place on a cooling rack. Set aside to cool completely.
While the bars are cooling, prepare the frosting. In a mixing bowl, beat together butter and cream cheese until combined. Then, add the powdered sugar, milk, vanilla extract, and salt. Beat for an additional 2-3 minutes until light and fluffy. Add food coloring and beat on low speed until combined.
Carefully pull the sugar cookie bars out of the baking pan, holding onto the edges of the parchment paper. Place on the cooking rack. Finally, spread the frosting on top of the sugar cookie bars and decorate with rainbow sprinkles. Refrigerate until ready to serve. Then, slice into 16 squares and enjoy!