Heat oven to 375 degrees. Line two baking large sheets with parchment paper.
Combine flour, baking powder, baking soda and salt in a bowl and whisk to blend.
In a large bowl or the bowl of a stand mixer, beat cream cheese, butter and sugar until fluffy.
Add egg and extracts and blend again.
Add flour mixture and beat just until flour disappears. In some cases, this dough will feel too soft to roll into balls in your hands; if so, let it chill in the fridge for 20 minutes or so before using.
Scoop balls of dough with large cookie scoop and roll them briefly in the palms of your hands before dropping them in a bowl of rainbow sprinkles and gently rolling to coat them evenly. I find that the sprinkles adhere much better to tacky exterior of balls of dough that have been briefly warmed by your hands — trust me here.
Transfer balls of sprinkle-coated dough to baking sheets at least two inches apart. Use the bottom of a drinking glass to press down on the cookies until they are about 1/4 to 1/2-inch tall. If you see any bare spots in the sprinkles that bother you, you can sprinkle a few more on top.
Bake for 9 to 10 minutes until they look underbaked but lightly golden underneath. [If they’re not quite soft in the center, they will be fully crisped through the next day.] Let set on the baking sheet on a rack for a few minutes before transferring to cooling racks to cool the rest of the way. Repeat with remaining cookie dough.