Place the softened butter, cream cheese, egg, and vanilla extract in a large mixing bowl. Beat the ingredients together until the mixture becomes fluffy, smooth, and thoroughly combined. Use either a hand mixer or stand mixer set to medium speed.
Gradually add the yellow cake mix to the prepared wet mixture. Continue blending until all of the dry mix has been incorporated and a smooth, uniform dough forms. The dough may become quite thick, so continue mixing until no dry portions remain.
Cover the mixing bowl with plastic wrap or a clean kitchen towel. Transfer the dough to the refrigerator and chill for 30 minutes to 1 hour. Refrigerating firms the mixture and makes it easier to shape.
Remove the chilled dough from the refrigerator and shape it into balls measuring approximately 1 inch in diameter. Roll each dough ball in festive sprinkles first, if using, until evenly decorated. Next, place each ball in powdered sugar and roll until the surface is completely coated.
Preheat the oven to 350°F (175°C). Arrange the coated dough balls on a parchment-lined baking sheet, leaving approximately 2 inches of space between each cookie.
Bake for 10–12 minutes, or until the edges are lightly browned. Avoid baking beyond this point.
Remove the baking sheet from the oven and allow the cookies to rest on the pan for approximately 5 minutes so they can firm slightly. Carefully transfer them to a wire cooling rack and leave them there until completely cooled.