Whisk together the flour, baking powder, and salt in a medium bowl, and set aside temporarily.
Combine the butter and granulated sugar in the bowl of a large stand mixer fitted with a paddle attachment. Mix the butter and sugar together at medium speed for 2-3 minutes until light and fluffy.
Turn the mixer to low, add the egg and vanilla extract, and mix until well-incorporated.
With the mixer still on low speed, slowly add the flour and mix until just a few streaks of flour remain. Stop the mixer, and finish scraping down the bottom and sides of the bowl with a rubber spatula. The dough should be soft and supple but not sticky.
Divide the dough into 3 equal parts. If you have a kitchen scale, each portion should be approximately 10 ounces.
Leave one portion uncolored, and use gel food coloring to color the other two portions red and green. You can stir the food coloring in by hand, knead it in like bread dough, or mix it in using the mixer.
Form each color into a disc and wrap them tightly in plastic wrap. Refrigerate for at least 45 minutes, until firm.
Roll each color out between two sheets of parchment to a long rectangle, approximately 6 x 13” long.
Stack the dough rectangles on top of each other in this order: green, white, then red on top. Roll the dough up into a long, tight spiral.
To roll the edges in sprinkles, brush the outside of the dough log with a very thin layer of corn syrup. Scatter the sprinkles on a baking sheet, and roll the log around the sprinkles, pressing it into the sprinkles so they adhere and it is completely covered.
Wrap the dough log in plastic wrap, and refrigerate for at least 45 minutes, or until firm.
Preheat the oven to 350 F, and cover 2 baking sheets with parchment.
Use a large, sharp chef’s knife to slice the log into rounds a little under ½” thick. Place them on the baking sheets with a few inches between each cookie.
Bake the cookies for 13-15 minutes, until they have spread and puffed, and no longer have a raw shine in the center.
Once cool, remove from the baking sheets and enjoy! Pinwheel cookies can be stored in an airtight container at room temperature and should be enjoyed within 4-5 days for maximum freshness.
