In a large mixing bowl, cream together unsalted butter and powdered sugar using an electric mixer on medium speed until light and fluffy, about 3 minutes.

Add eggs and milk, mixing until smoothly combined.

Gradually incorporate flour, salt, and extracts until a soft dough forms.

Divide the dough into three portions and tint one portion purple using gel food coloring.

Split the remaining dough into half, leaving one half white and tinting the other black.

On a floured surface, roll out the black and white dough halves into rectangles about 1/4-inch thick.

Stack the white rectangle on the black and roll gently to blend edges.

Roll out the purple dough into a long rectangle, spread with purple sprinkles, and roll tightly into a log.

Position the purple log at one end and roll the black-and-white stack around it tightly.

Wrap the log in plastic wrap and chill in the refrigerator for at least 1 hour.

Preheat the oven to 375°F (190°C) and roll the chilled log in sprinkles before slicing into rounds about 1/2-inch thick.

Place slices on a parchment-lined baking sheet and bake for 10 minutes or until edges are lightly golden.