In a medium bowl, mix flour, baking soda, and salt. In a large bowl, cream the butter, cream cheese, sugar, and powdered sugar until thoroughly combined. Stir in egg and vanilla and mix for about 1 minute.
Add the dry ingredients to the wet ingredients and mix on medium-low until combined into a crumbly but wet texture.
Form small balls of dough and dip into sprinkles. Lay on a greased cookie sheet and flatten. Cook for 10 minutes and allow at least 5 minutes to cool.