Preheat oven to 350°F. Line two sheet pans with parchment paper. In a medium size bowl, whisk together the flour, baking powder, baking soda, cream of tartar, salt, and set aside.
In a standing mixer or a large bowl with a hand mixer, beat the butter and sugar on medium-high speed until pale and fluffy, about 1 minute. Add the egg and vanilla extract, scrape down the sides and bottom of the bowl if needed and beat until combined.
Reduce to low speed and mix in the dry ingredients. Pour in the sprinkles and chocolate, then mix until just combined.
Using a medium cookie scoop (1.75 inch) or 1 ½ tablespoons of dough, scoop and roll the cookie dough into balls. Place on the parchment paper lined cookie sheets with generous space between cookies. Bake for 12 minutes and let cool for a 5-8 minutes on the cookie sheet before transferring to a wire rack to finish cooling.
While the cookies bake, prepare the frosting. In a standing mixer or in a medium bowl with a hand mixer, beat the butter on medium-high speed until pale and fluffy. Reduce to low speed, add the vanilla and gradually add the confections sugar. Increase the speed to medium-high and beat until smooth.
Once the cookies are completely cool, about 15 minutes, spread about 1 tablespoon of frosting on each cookie. Finish with a sprinkle of your favorite colorful sprinkles!