*Make two half-batches of peppermint butter cookie dough: One half batch without red food coloring and one with red food coloring to yield one plain dough log and one red dough log.

First Half-Batch: In a mixer bowl fitted with the paddle attachment, beat half the butter, half the powdered sugar, and half the salt on medium speed for 2 minutes until creamy. Add ½ egg, half tsp vanilla extract and 1 tsp peppermint and beat for about 30 seconds until combined. Add flour and beat on low speed just until combined. Do not over mix the dough. If dough is too dry, add water, 1-2 teaspoons at a time. To check if the dough is done, take a piece of dough and press it between your thumbs – the dough should stick well together without feeling dry.

On a lightly floured surface, work the dough until it comes together. Shape into a log that is 1.5 inches in diameter. Wrap log in plastic wrap and refrigerate or freeze for at least 1-2 hours until firm. Dough can be left in the refrigerator for up to 3 days or in the freezer for 2 months.

Repeat step 2 and 3 with the second half-batch, adding red food coloring to the wet ingredients or red beet powder (for natural dye) to the flour before adding.

Preheat oven to 350°F/180°C. Line 2 pans with parchment paper.

Once the dough is cold enough, use a sharp knife to slice the log in half lengthwise to give you two long half-logs. If the dough is too crumbly and breaks, leave it for a few minutes to soften. Cut the half-logs lengthwise into thirds by cutting at a 60 degree angle and a 120 degree angle. Essentially, cut a V shape into the half-log. Repeat with your second dough log. You should have 6 equal-sized triangle-shaped long dough slices of each color. **

Create two new dough logs by alternating 3 red and 3 white pieces for each log. Gently squeeze the pieces together and lightly re-roll the log so it is smooth.

Then begin to slice each log into ¼-inch thick coin-shaped rounds. If you roll the log a quarter turn every time you cut, it keeps the log nice and round. If the dough feels too soft while cutting, wrap it with plastic wrap and chill it in the refrigerator for 15 minutes.

Arrange cookies on prepared baking sheets, placing them 1-2 inches apart. Bake for 10-12 minutes or until slightly golden brown around the edges. When done, the cookies should appear soft and bright. Allow cookies to cool on the pan for 10 minutes and then transfer to a wire rack to cool completely.

In the bowl of a stand mixer, beat the butter until soft and light, about 2 minutes on medium speed. Add powdered sugar and beat until well combined, about 2 more minutes. Scrape down the sides of the bowl. Add heavy cream or milk and peppermint extract and beat for another minute.

Using a pastry bag, pipe 1-2 teaspoons of frosting onto the centers of half the cookies. Sandwich the frosting down by placing the unfrosted half of the cookies on top of the frosting until it oozes to the sides perfectly. Roll the frosted edges in crushed peppermint candies.

Store cookie sandwiches at room temperature in an airtight container for up to 5 days or in the fridge for up to 2 weeks, bringing to room temperature before serving. Cookies can also be frozen for up to 2 months.