In a medium mixing bowl, mix together the flour, baking powder, and salt, Set aside.
In a large mixing bowl, beat together the butter and sugar for 1-2 minutes, or until pale and fluffy. Add the egg and vanilla to the butter mixture and beat until combined, scraping the sides of the bowl as needed.
Add the dry ingredients to the wet ingredients in two additions, mixing until just combined after each addition. Scrape the sides of the bowl as needed.
Divide the dough into 3 equal pieces and roll each piece into a ball. (You can eyeball it or use a kitchen scale to measure the pieces.)
Place one piece of dough back in the bowl and add the red food coloring. Beat with your mixer until the color is completely incorporated. (Be sure to use a bowl that won't stain.) Clean your mixer paddle or hand mixer blades.
Place one piece of dough back in the bowl and add the green food coloring. Beat with your mixer until the color is completely incorporated. Leave the third piece of dough as-is.
Press each piece of dough into a flat square and wrap in plastic wrap. Refrigerate the dough for 1 hour or until firm.
Remove the dough squares from the fridge. Place the red dough between 2 sheets of parchment paper or waxed paper. Use a rolling pin to roll out the dough to a 10-inch square. Leave dough between parchment.
Repeat with the other 2 pieces of dough. Refrigerate cookie dough for 30 mins.
Remove dough from the fridge, and take the top layer of parchment off each sheet of cookie dough. Place the red dough down on a counter. Top with the white dough, non-parchment sides touching. Be sure to try and line up the edges of the dough as much as possible.
Remove the parchment from the white dough. Top the white with the green, non-parchment sides touching, being sure to line up the edges. Remove parchment from the green dough. Use a pizza cutter to trim the left and right edges of the cookie dough into straight lines.
Very carefully, starting with one of the straightened sides, roll the dough into a long shape until you reach the other trimmed dough edge. Use the parchment paper to lift the dough to get it started. Once the dough log is complete, gently pinch the seam closed along with any breaks on the outer red layer.
Wrap the dough log in plastic wrap and refrigerate for 1 hour or until firm.
Preheat your oven to 350 degrees F. Line a baking sheet with a silicone mat or parchment paper.
Use a sharp knife to cut the dough log into 1/4-inch thick slices. (Discard the ends since they don't make a nice pinwheel design.) Place the cookies on your prepared baking sheets and bake for 12 to 15 minutes, or until the cookies are set.
Carefully remove from the oven and let cool for 5 minutes on the baking sheet before transferring to a wire rack to cool completely. Serve immediately or store in an airtight container until ready to serve.