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.
Both methods: Scoop balls of dough 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.
Transfer balls of sprinkle-coated dough to baking sheets at least two inches apart