In a large bowl using a handheld 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 and beat until fluffy and light in color. Beat in egg, egg yolk, and vanilla. Scrape down the sides and up the bottom of the bowl as needed.

In a medium bowl, whisk the flour, baking soda, cream of tartar, cornstarch, and salt together until combined. 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 and will be a little crumbly at first. But if you keep mixing, the dough will come together. Once combined, gently beat in the sprinkles on low speed until evenly disbursed. Cover the cookie dough tightly and chill in the refrigerator for at least 3 hours and up to 3 days. Chilling is mandatory. Alternatively, you can roll the cookie dough into 1.5 Tablespoon balls and chill on a cookie sheet (covered) and then bake as directed in the next step.

Remove cookie dough from the refrigerator and let sit out at room temperature for at least 15 minutes. If the cookie dough chilled longer than 3 hours, allow to sit at room temperature for 30-40 minutes. This makes it easy to handle, while still keeping a firm texture from chilling. Preheat oven to 325°F (163°C) and line 2 large cookie sheets with parchment paper or silicone baking mats. Roll cookie dough into balls, about 1.5 Tablespoons of dough in each ball (a medium cookie scoop is helpful for this), and set on cookie sheet—about 8-9 cookies per sheet. Bake in batches for 11-12 minutes or until the edges are slightly browned. The cookies will still appear very soft in the centers. That’s ok; they’ll set up and become firmer as they cool. Allow the cookies to cool on the cookie sheets for 3 minutes, then move to a wire rack to cool completely.

In a large bowl using a handheld mixer or stand mixer fitted with a paddle attachment, beat the butter on medium speed until creamy—about 2 minutes. Add confectioners’ sugar, cream, vanilla extract, and salt with the mixer running on low. Increase to high speed and beat for 3 full minutes. Add more confectioners’ sugar if frosting is too thin, more cream if frosting is too thick, or a pinch more of salt if frosting is way too sweet.

Frost the cooled cookies as desired and decorate with more sprinkles. Store cookies in an airtight container at room temperature for up to 3 days or in the refrigerator up to 6.