In a medium bowl, whisk together the all-purpose flour, baking powder, and salt; set aside. In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy, about 3 to 4 minutes. Add the egg and vanilla extract, and mix until fully incorporated. Gradually add the dry ingredients to the wet mixture on low speed, mixing until a soft, uniform dough forms.

Divide the dough evenly into three portions. Leave one portion plain for the white layer. Add red food coloring to the second portion and mix until evenly colored. Add green food coloring to the third portion and mix thoroughly. If any portion feels too firm, add 1 tablespoon of milk to soften slightly.

Roll each dough portion between two sheets of parchment paper into a rectangle about ¼ inch thick and similar in size. Transfer each rolled dough sheet to a baking sheet and chill for 30 minutes to help firm the layers for assembly.

Remove the dough sheets from the refrigerator once firm. Stack the green dough over the white dough, then the red dough over the green, aligning edges closely. Use a rolling pin to gently press the layers together. Starting from one edge, tightly roll the layered dough into a log to create the spiral shape.

Wrap the dough log in plastic wrap and refrigerate for at least 2 hours or overnight until firm.

Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper. Using a sharp knife, slice the chilled dough log into ¼ inch thick rounds. Arrange slices 2 inches apart on the prepared baking sheets.

Bake for 10 to 12 minutes, or until the edges are set but not browned. Let cookies cool on the baking sheet for several minutes before transferring to a wire rack to cool completely.