Cream the butter and powdered sugar in a mixing bowl until light and fluffy, about 3 minutes. Add eggs and milk, mixing until combined.

Divide the dough into three portions. Color one with purple gel food coloring, leave one plain (white), and color the last with black gel food coloring.

Roll out black and white dough into 6x12-inch rectangles. Stack them, press together, and gently roll with a rolling pin.

Roll out the purple dough into a 6x12-inch rectangle, sprinkle with purple sprinkles, and roll into a tight log.

Position the purple log at one end of the black-and-white dough rectangle and roll tightly around it to form a spiral shape.

Roll the formed log in purple and black sprinkles, wrap tightly, and refrigerate for at least 1 hour.

Preheat the oven to 375°F (190°C). Slice the log into ¼-inch rounds and bake for about 10 minutes until edges are set.

Cool on the baking sheet for 10 minutes before transferring to wire racks to cool completely.