Preheat the oven to 350°F. Line two baking sheets with parchment paper and set them aside.
Using a stand mixer or hand mixer and large bowl, cream together butter, shortening, and sugar until light and fluffy (4-5 minutes).
Beat in eggs, vanilla, and instant pudding mix.
In another bowl, whisk together flour, baking powder, and salt. Gradually add to the butter mixture, a little at a time, mixing between additions.
Place sprinkles in a small, shallow bowl. Using a cookie scoop or a heaping Tablespoon, scoop cookie dough out and roll in your hands to form a ball. Place the dough ball in the bowl of sprinkles and roll to coat in sprinkles. Place onto prepared cookie sheets, about 2 inches apart.
Bake for 12-15 minutes or until set and lightly golden brown around the edges. Allow the cookies to cool on the cookie sheet for 5 minutes, then transfer to a cooling rack to cool fully.
Notes
Storage: Store fully cooled cookies in an airtight container at room temperature for up to 5 days. For longer storage freeze cookies for up to 3 months.Make ahead: The cookie dough can be prepared ahead of time and refrigerated until ready to bake, up to 3 days. Or the cookie dough can be frozen for up to 3 months.