Cream the butter and powdered sugar in a large mixing bowl until fluffy and light in color, about 3-5 minutes. Add eggs and milk, mixing until combined. Gradually incorporate flour, salt, and vanilla extract until a soft dough forms.

Divide the dough into three portions; keep one plain, color the second half purple, and divide the last portion into two: one to remain white, the other to be colored black. Knead each section until the colors are vibrant.

Roll the black and white dough into 6x12 inch rectangles. Stack the white layer on top of the black layer and roll tightly from one end to create a log.

Roll out the purple dough into a rectangle matching the size of the black-and-white layers. Sprinkle with purple sprinkles and roll tightly to form a log.

Position the purple log at one end of your black-and-white layers and roll tightly to encase the purple center, forming a single large spiral.

Wrap the cookie log in plastic wrap and chill in the refrigerator for about 1 hour. Once chilled, roll the log in black or chocolate sprinkles for a crunchy texture.

Preheat your oven to 375°F (190°C). Slice the chilled log into 1/4-inch rounds and arrange them on a parchment-lined baking sheet. Bake for 10 minutes or until the edges are lightly golden.

Allow the cookies to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.