In a stand mixer fitted with the paddle attachment, mix the butter and sugar together until just incorporated. Do not over-mix at this stage, or the cookies may spread while baking.
Add the egg and vanilla extract. Mix again on low speed, stopping to scrape down the sides of the bowl intermittently as needed.
In a medium bowl, whisk together the flour and salt. Add to the butter and egg mixture. Mix on low speed until a dough is formed and there are no longer any streaks of butter in the mixing bowl. The dough will often clump around the paddle attachment while being mixed. This is normal and a good sign that your dough is the right consistency. If your mixture does not come together and is crumbly, add ice cold water 1 tbsp. at a time until the dough clumps.
Turn the dough out onto a sheet of wax paper. Divide in half. Return one half of the dough to the mixing bowl and add the peppermint extract and 1/2 teaspoon gel food color. Beat until well combined. Add more food color if needed to create a deep red hue. If the mixture becomes sticky, add additional flour 1 tablespoon at a time until it can easily be handled. Shape the red dough into a ball; shape the white dough into a ball. Cut each ball in half.
Briefly knead one white portion and one red portion together – do not over mix. Only knead until the dough is combined and there are definite swirls of red and white color. Roll into a log and wrap in waxed paper. Repeat with the remaining red and white dough portions so that you have two marbled dough logs. Refrigerate the cookie dough logs until firm, about 30 minutes.
Line one or more large baking sheets with parchment paper.
Cut the chilled cookie dough into coins about 1/4 inch thickness and place them on the cookie sheets 1 1/2 inches apart. Refrigerate the cutouts for 10 minutes. This will help the cookies maintain a crisp shape during baking.
Preheat the oven to 350°F.
Bake the cookies for 10-12 minutes, or until faintly golden around the edges of the white part of the cookies. Remove from the oven when done, and while the cookies are still hot, press a single silver dragée into the centers of each cookie. (Don't add the dragees to the cookies before baking, some brands will melt away under high heat.)
Let the cookies cool on the baking sheet for 5 minutes. Transfer to a wire rack to cool completely. Store cookies in an airtight container, or package them for gift-giving.
Keyword butter cookie dough, peppermint extract, slice and bake