In a large bowl, cream butter and sugars until light and fluffy. Add egg and vanilla. Combine the flour, baking powder, salt and baking soda; gradually add to creamed mixture and mix well.
Divide dough into three portions; tint each a different color. Roll each portion of dough on waxed paper into a 9x5-in. rectangle. Freeze for 10 minutes.
Cut each rectangle in half lengthwise. Lightly brush top of one rectangle with milk. Top with another colored dough. Remove waxed paper; brush top with milk. Repeat with remaining dough, alternating colors to make six layers. Press together lightly. Wrap with plastic wrap. Refrigerate for several hours or overnight.
Unwrap dough; cut into 1/4-in. slices. Place 2 in. apart on ungreased baking sheets. Bake at 350° for 8-10 minutes. Cool for 1-2 minutes before removing from pans to wire racks to cool completely.