In the bowl of your stand mixer, or a medium-large bowl with your hand mixer, cream together your butter and sugar until light and fluffy.
Add your egg and vanilla, and beat until well combined.
Add salt and flour and stir together until just combined.
Divide your dough into 3 equal portions in smaller bowls.
Add green food coloring to one and red to another, leaving the third. Mix until dough is adequately colored to your liking. I used about 3-5 drops of color in each.
Flatten each bowl of dough into a small disc, and wrap tightly with cling wrap. Place in the refrigerator to chill for 1 hour.
After chilling, remove dough lightly flour and roll out dough into approximately a 7 inch by 9 inch rectangle. The dough should be somewhere between ¼ and ⅛ inch thick. I found this easiest to do on parchment paper on top of a silicone mat so the parchment doesn't slide.
After each piece of dough is rolled out, stack the three rectangles. I chose to have white dough in the center, and green to be the outer dough but it's completely personal preference and makes no difference.
Roll the dough into a spiral log like you would cinnamon roll dough, on the long edge.
Dump your sprinkles into a platter or cookie sheet and place the dough log into it and gently roll it to coat the sides with sprinkles.
Wrap your cookie dough in cling wrap tightly and place in the refrigerator to chill for at least 1 hour. I generally chill mine overnight.
When you are ready to bake your cookies, preheat your oven to 350°F. Wait until your oven is completely ready before taking the dough out. Line a baking sheet with parchment.
Take your dough out and slice your cookies. They can be as thin or thick as you'd like, but I sliced mine at about ¼" thick, which is what bake time is based off of.
Any cookies not being placed onto the cookie sheet to bake immediately should be placed back in the refrigerator between batches.
Place sliced cookies on your cookie sheet, and bake for about 10 minutes on the center rack of your oven. If you have a color other than the white dough on the outside you won't be able to tell any browning, but the top of the cookies should look set and no longer have a sheen.
Remove cookies from oven and transfer to a wire cooling rack.
Store cookies in an airtight container for up to a week. Enjoy!