Cream the butter and sugar by beating together 1-1/2 cups of unsalted butter and 2 cups of powdered sugar for about 2 minutes until light and fluffy.

Incorporate wet ingredients by adding 2 eggs and 2 tablespoons of milk to the mixture and continue to mix until just combined.

Mix in the dry ingredients gradually by adding 3-1/2 cups of all-purpose flour and 1/2 teaspoon of salt, stirring gently until fully incorporated.

Divide the dough into three portions, color half purple and split the other half into black and white sections using gel food coloring.

Roll out the black and white dough to form a 6x12-inch rectangle, layer them together to create contrast.

Roll out your purple dough into a thick rectangle, sprinkle purple sprinkles and roll it into a log shape.

Encase the rolled purple log with the layered black and white dough, forming a larger log and sealing the edges well.

Chill the encased log in plastic wrap for at least 1 hour to firm.

Preheat the oven to 375°F (190°C) while the dough chills, then slice the chilled log into 1/4-inch thick rounds.

Bake the cookies on a lined baking sheet for about 10 minutes, allowing them to cool for 10 minutes before transferring to a wire rack.