Preheat oven to 350℉.
In the mixing bowl of a stand mixer, using the whisk attachment, add the butter, sugar, vanilla, and egg. Mix until light and fluffy.
Add the sprinkles to the butter mixture.
In a separate medium mixing bowl, add the flour and baking powder, and stir well.
Next, add the flour mixture to the butter mixture - adding the flour a little at a time until all is incorporated and blended.
Remove the whisk attachment, and use the paddle. Continue to blend the cookie dough until it's completely blended and a smooth ball starts to form. Scrape down the mixing bowl as needed.
Next, line two cookie sheets with parchment paper, and roll the cookie dough into small balls, about 1 inch balls, and place the balls on the parchment paper.
Bake at 350℉ for about 15 minutes, or just until the cookies start to turn a light golden brown around the edges. About half way through baking the cookies, check the cookies. When you see they have cracked a little, remove the trays.
Take a flat bottom glass and dip it in white sugar before lightly applying to each cookie - smash the cookies very gently, making them a little flatter so they spread out a little more. This will give the cookies the crinkle look. Return the pans to the oven to finish the baking time.
When the cookies are done, remove from the oven to a wire rack to cool completely. While cookies are cooling, make the frosting.