In a medium bowl, mix flour and salt; set aside. In large bowl, cream butter and sugar until light and fluffy.
Stir in the egg, then corn syrup and vanilla extract. Gradually add in flour mixture until just combined.
Divide dough into three even sections (just over 10 ounces each). Add red food coloring to one section to desired hue, add green food coloring to another section to desired hue and leave the third one white. Pat into disks; wrap in plastic wrap and refrigerate for 30 minutes to an hour.
One color at a time, roll dough between two sheets of parchment paper or waxed paper into rectangles, approximately ¼-inch thick.
Stack the three rectangles of dough with white in the middle. Slice the stacked rectangles in half. This is so that we can make some of the pinwheel Christmas cookies with red on the outside and some with green on the outside.
Roll one cut section from one end to the other to form a log; set aside. Carefully flip the other section of dough upside down so that the opposite color is on top. Then roll into a log. Trim the uneven ends off. Don't worry if the logs look crazy or not perfectly even; trust me, the cookies will be great!
Spread Christmas sprinkles onto a rimmed baking sheet and gently roll each log over the sprinkles to coat. Wrap in plastic wrap and refrigerate 30 minutes.
Cut each log into even slices up to ½-inch thick. (If your ends yield slightly smaller cookies, like mine, that's totally fine! I just try to bake mostly same-sized cookies together on a single tray, then bake the smaller ones separately at the end.
Lay on a parchment paper-lined cookie tray and bake for about 12-15 minutes until edges start to turn golden brown and cookies are set. Leave on cookie sheet for a couple of minutes before transferring to wire rack to cool completely.
Storage: Store in an airtight container at room temperature for up to three days or freeze for up to a month.
Notes
Weigh it Out: To help ensure your pinwheel swirls are as even as possible, use a kitchen scale to divide the dough into three equal sections.
Chill the Dough: After mixing and before rolling, chill the dough for at least an hour. This helps the dough firm up, making it easier to handle and preventing excessive spreading when baked.
Use Parchment Paper: Roll the dough between sheets of parchment paper to prevent sticking and make the rolling process smoother.
Even Thickness: Aim for an even thickness while rolling out the dough to ensure consistent swirls throughout the cookies.
Tight Rolling: When forming the dough into a log, roll it tightly to create well-defined swirls in the cookies. (I always have a few air gaps, so don't stress about it!)
Chill Before Slicing: After rolling the dough log, chill it again before slicing. This helps maintain the shape of the cookies and prevents them from unraveling while cutting.
Sharp Knife: Use a sharp knife for slicing the dough to ensure clean, precise cuts without squishing the dough.
Adjust Food Coloring Amount: Start with a small amount of food coloring gel and gradually increase until you achieve the desired color intensity. Remember, you can always add more but can't remove excess coloring.
Same-size: Bake same-size cookies together on a single sheet. Sometimes the end will yield smaller cookies, so if they're much smaller, you may want to bake those separately so they don't overbake. You could discard the small ones, but I don't like to waste anything, so I just bake them separately.
Experiment with Variations: Feel free to experiment with different colors and sprinkle styles to suit various occasions or themes beyond the holiday season.