In a large mixing bowl, cream together the butter and powdered sugar until light and fluffy, about 3 minutes. Beat in the eggs and milk until combined. Gradually stir in flour, salt, and extract to form a soft, cohesive dough.

Divide the dough into three equal portions. In one portion, add purple gel food coloring and mix well. Leave one portion plain, and tint the third portion black.

On a floured surface, roll out the black and plain dough into 6x12-inch rectangles. Layer the plain on top of the black and roll into a log, ensuring a smooth seam.

Roll the purple dough into a 6x12-inch rectangle and sprinkle in purple sprinkles. Roll it into a log shape carefully, keeping sprinkles inside.

Position the purple dough log at one end of the black-and-white layered dough and roll it around the purple log until completely encased, sealing the edges well.

Wrap the assembled dough log in plastic wrap and refrigerate for at least 1 hour. After chilling, roll it in black or chocolate sprinkles, coating it evenly.

Preheat oven to 375°F (190°C) and line a baking tray. Slice the log into ¼-inch rounds and place on the tray with a little space in between. Top each slice with extra sprinkles.

Bake cookies for about 10 minutes or until edges are lightly golden. Let cool on the tray for 10 minutes before transferring to a wire rack to cool completely.