Prepare the cookie dough by creaming together the butter and powdered sugar until fluffy. Beat in eggs and milk, then gradually mix in flour and salt.

Divide the dough into three parts; color one part purple and leave one part white. Divide the white part in half and color one half black.

Roll out the black and white dough into rectangles, stack them, and encase the purple dough around them to form a log.

Chill the dough log in plastic wrap in the refrigerator for at least 1 hour.

Preheat the oven to 375°F (190°C). Slice the chilled log into 1/4-inch rounds, place on a lined baking sheet, and sprinkle with additional sprinkles before baking for 10 minutes.

Cool the cookies on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.