Whisk together 2 cups all purpose flour, 1 teaspoon baking powder, and 1/2 teaspoon kosher salt in a medium bowl. Set aside.
Add the 2 sticks (8 oz) unsalted butter, 1/2 cup granulated sugar, and 1/2 cup packed light brown sugar to the bowl of a stand mixer. Cream together the butter and sugar on medium-high speed until light and fluffy, about 3 minutes. Add 1 large egg and beat on medium-high speed until light and fluffy, about 2 more mintues. Add the 1 teaspoon vanilla extract and 1/2 teaspoon peppermint extract and mix until fully incorporated, about 1 minute.
Add the flour mixture to the bowl of the stand mixer. Mix on low speed until incorporated, about 1-2 minutes. Remove half of the dough from the bowl and set aside.
Add a few drops of red food coloring to the remaining dough in the stand mixer and mix on low speed until incorporated, scraping down the sides of the bowl as needed. Add additional food coloring as needed until you get the color you want.
Place the half of the dough without the food coloring between two sheets of parchment paper and roll into a rectangle. Repeat with the second half of the dough, rolling into a rectangle roughly the same size and shape as the first.
Lay one piece of dough on top of the second, and roll the pieces together to make one rectangle (make sure not to roll too aggressively so that the colors mix together). Roll the rectangle away from yourself into a tight log (as if you were making cinnamon buns). Wrap the dough log tightly with plastic and refrigerate for at least an hour or up to 2 weeks.
Heat oven to 350°F. Prepare 2 baking sheets by lining with parchment paper or silicone baking mats. Roll the cookie dough log in crushed candy canes or sanding sugar if desired . Slice the log into 1/2" (1cm) slices. Place the slices on the prepared baking sheets 1 inch apart. Bake until just beginning to brown, about 13-15 minutes. Cool on the baking sheet. Store in an airtight container or zipper bag at room temperature for up to two days, or in the freezer for up to 2 months.