Step 1: In a large bowl or stand mixer with the paddle attachment, cream together the softened butter and granulated sugar until light and fluffy.
Step 2: Beat in the egg and vanilla extract until well combined, scraping down the sides of the bowl as needed.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Do not overmix.
Step 4: Divide the dough into 2-4 equal portions, depending on how many colors you plan to use. Tint each portion with a different gel food coloring, kneading gently until the color is evenly distributed. Leave one portion plain if you want a white layer.
Step 5: On separate pieces of parchment paper, roll each colored dough into a rectangle, approximately 9x12 inches and about 1/8 inch thick. If the dough is too sticky, chill it for 10-15 minutes before rolling.
Step 6: Carefully stack the rolled-out dough rectangles on top of each other, peeling them gently off the parchment. Trim the edges to create a neat stack. You can lightly brush a tiny bit of water or egg white between layers if needed, but the dough should adhere naturally.
Step 7: Starting from one of the long sides, carefully roll the stacked dough into a tight log. Press gently to eliminate any air pockets. Wrap the dough log tightly in plastic wrap.
Step 8: Chill the dough log in the refrigerator for at least 1-2 hours, or until very firm. This is crucial for easy slicing and maintaining the spiral shape.
Step 9: Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper.
Step 10: Using a sharp chef's knife, slice the chilled dough log into 1/4-inch thick rounds. Place the cookies about 1 inch apart on the prepared baking sheets.
Step 11: Bake for 10-12 minutes, or until the edges are lightly golden. The centers should still be slightly soft. Remove from the oven and let cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.