In a small bowl, combine flour and salt. Set aside.
In a stand mixer with the paddle attachment, beat the butter on high speed until light and fluffy, about 4-5 minutes. Scrape the sides, add the granulated sugar and powdered sugar and continue to beat until very light in color and fluffy, another 2-3 minutes. Scrape sides again and add the egg yolks, peppermint extract and vanilla, beat on low speed until well combined.
With the mixer running on low speed, spoon in the flour and salt mixture until all of the dry ingredients have been added and fully combine. Do not over mix.
At this point, remove half of the dough and place on a sheet of plastic wrap. If you're a perfectionist, you should have about 28 ounces total, so you'd want to take out about 14 ounces of the dough. Add food coloring to remaining dough in bowl and mix just until the color has evenly blended in. Add the red dough to a separate piece of plastic wrap.
Shape both dough balls into a square that's about 5-6 inches in length. Wrap tightly in plastic wrap and refrigerate 2 hours or overnight (or longer if you're making them ahead of time).
Preheat oven to 325 degrees F and prepare two baking sheets with parchment paper or a silpat.
Roll each dough to a 9x9 inch square, then stack them on one another and roll to seal them together. Cut the dough down the center and refrigerate both halves. After the dough has chilled a bit, after maybe 15 minutes, take out one of the halves and start cutting short strips that are about ¼ inch thick. Roll each strip to lengthen and slightly twist at the same time. Roll in decorating sugar and then lay out on baking sheet in the shape of a candy cane. Refrigerate or freeze the baking sheet until the dough is cold again prior to baking (this will help prevent them from spreading while they bake).
Bake until just slightly brown on the bottoms, 13 to 15 minutes. Rotate your baking sheet half way though if your oven doesn't bake evenly. Remove from oven and allow to cool on sheets for 5 minutes before transferring to cooling rack. Continue baking process with remaining dough, keeping it cool until ready to bake (otherwise your cookies expand too much).
Store in airtight container and segregate from other cookies as the peppermint flavor will transfer.