In a large bowl, cream together softened butter and sugar on medium speed for 3-4 minutes until light and fluffy with a pale yellow color. Add the egg and vanilla extract, then beat on low speed until fully incorporated and smooth.
In a separate bowl, whisk together flour, salt, and baking powder. Gradually add the dry ingredients to the butter mixture, mixing on low speed just until the dough comes together and no flour streaks remain. Shape into a flat disk, wrap tightly in plastic wrap, and refrigerate.
In a clean large bowl, cream together softened butter and sugar on medium speed for 3-4 minutes until light and fluffy. Beat in the egg and vanilla extract on low speed until smooth and well combined.
In a separate bowl, whisk together flour, cocoa powder, salt, and baking powder until no lumps remain. Gradually add to the butter mixture, mixing on low speed until a uniform dark brown dough forms. Shape into a flat disk, wrap tightly, and refrigerate alongside the vanilla dough for at least 30 minutes.
Remove both doughs from the refrigerator and let sit at room temperature for about 5 minutes. Place a large piece of parchment paper on your work surface and lightly dust with flour. Roll the vanilla dough into a 12x10-inch rectangle about ¼ inch thick, using even pressure and rotating occasionally. Transfer with parchment to a baking sheet and set aside.
Repeat the same rolling process with the chocolate dough, aiming for the same 12x10-inch dimensions and ¼-inch thickness. The more similar they are in size and thickness, the better your spirals will look.
Remove the top sheet of parchment from the chocolate dough, then carefully flip it onto the vanilla dough so the two rectangles are stacked perfectly. Gently peel away the parchment now on top and press the layers together gently, especially at the edges, to eliminate air pockets.
Starting from one of the longer sides, carefully roll the layered dough into a tight log, lifting the bottom parchment paper to help guide the roll and keeping it as even and tight as possible. The log should be about 12 inches long and 2 inches in diameter. Wrap tightly in plastic wrap, twisting the ends to secure.
Place the wrapped dough log in the refrigerator and chill for at least 3 hours, preferably overnight. For faster results, freeze for 1-2 hours until firm enough to slice cleanly. Wrapped logs can be frozen for up to 3 months.
Preheat oven to 350°F (175°C) and position racks in the upper and lower thirds. Line two baking sheets with parchment paper or silicone baking mats. Remove the chilled log from the refrigerator and let sit at room temperature for about 5 minutes to prevent cracking.
Unwrap the dough log and place on a cutting board. Using a sharp knife, slice into rounds approximately ¼ inch thick using a gentle sawing motion rather than pressing straight down. Rotate the log slightly after every few slices. If dough becomes too soft, return to the refrigerator for 15-20 minutes.
Arrange sliced cookies on prepared baking sheets, spacing about 2 inches apart. Bake for 10-12 minutes, or until edges are just set and lightly golden. Rotate baking sheets halfway through for even browning. Cookies will feel slightly soft when first removed but firm up as they cool.
Let cookies cool on the baking sheet for 5 minutes to set up. Using a spatula, carefully transfer to a wire cooling rack to cool completely. Once cool, cookies will have crisp edges with a tender center.