Preheat oven to 350F degrees. Line an 8-inch square baking pan with aluminum foil, making sure to leave enough overhang on the sides. Set aside.
In a large bowl using a hand-held mixer or stand mixer fitted with a paddle attachment, cream the softened butter for about 1 minute on medium speed. Get it nice and smooth, then add the sugar on medium speed until fluffy and light in color. Beat in egg, egg yolk, and vanilla. Scrape down the sides as needed.
In a medium bowl, whisk together the flour, salt, baking powder, baking soda, and cornstarch. With the mixer running on low speed, slowly add the dry ingredients to the wet ingredients in 3 different parts. The dough is quite thick.
Press the cookie dough evenly into the prepared baking pan. Bake for 25-26 minutes or until very lightly browned on top. You want the cookie bars to be extra soft, so careful not to overbake. Allow the bars to cool completely on a wire rack at room temperature before frosting. The center will slightly sink - that's normal.
When completely cool, frost with a thick layer of frosting and make sure to top with sprinkles!