Cream the unsalted butter and powdered sugar together in a mixing bowl until fluffy and light. Mix in the eggs and milk, followed by the flour, salt, and extracts until a soft dough forms.

Split the dough into three portions. Color one with purple gel food coloring, another with black gel food coloring, and leave the last portion plain.

Roll out the black and white dough into 6×12-inch rectangles. Stack the white layer on top of the black layer, then lightly roll them together.

Roll out the purple dough into another rectangle, sprinkle it generously with purple sprinkles, and roll it tightly into a log.

Place the purple dough log at one end of the black-and-white layered dough. Gently roll to enclose the purple log, forming a large spiral log.

Roll the spiral log in sprinkles to coat the outside. Wrap tightly in plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 375°F. Carefully slice the chilled log into ¼-inch rounds and bake for about 10 minutes until the edges are set.

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