• Position an oven rack in the middle of the oven and preheat to 350F [180C]. Grease a 9 by 13 in [23 by 33 cm] baking pan and line with a parchment sling.
• In a medium bowl, whisk together the flour, baking powder, baking soda, and cream of tartar.
• In the bowl of a stand mixer fitted with a paddle, beat the butter on medium speed until creamy, about 1 minute. Add the granulated sugar and salt and beat on medium speed until light and fluffy, 2 to 3 minutes. Add the eggs, egg yolk, and vanilla and beat on medium speed until combined. Add the flour mixture and beat on low speed until just combined.
• Transfer the dough to the prepared pan and use your hands to smooth it into an even layer (a greased piece of plastic wrap can also work well).
• For soft, chewy bars, bake for 23 to 25 minutes, until light golden brown and a wooden skewer comes out clean. For bars with crisp tops and bottoms, bake for 28 to 32 minutes, until the bars are golden brown. Transfer the pan to a wire rack and let cool completely.

For the cream cheese frosting

• In the bowl of a stand mixer fitted with a paddle, beat the cream cheese, butter, vanilla, and salt on low speed for 2 to 3 minutes, until smooth, creamy, and combined. Gradually add the confectioners' sugar and mix on low speed until combined and smooth, stopping to scrape down the sides of the bowl as necessary.
• Use an offset spatula to evenly coat the cooled bars with the frosting. Before the icing sets, cover with sprinkles, if desired.
• Use the parchment sling to gently lift the bars from the pan. Cut into squares and serve. The bars can be stored in an airtight container in the refrigerator for up to 3 days.