Preheat oven to 350°F. Line 24 muffin tins with paper liners and set aside.
Prepare cake mix as instructed on the box, adding the peppermint extract. Once batter is prepared, pour half into a separate bowl and add red food coloring until desired shade of red is reached.
Fill prepared muffin tins with batter, alternating spoonfuls of red and white until tins are 2/3 full. Bake for about 15 minutes, until tops spring back when lightly touched in the center. Let cool in pan for about 10 minutes before removing to wire rack to cool completely.
In the bowl of your mixer, beat butter, milk, and peppermint extract on medium speed until smooth.
With the mixer on low, slowly add powdered sugar, beating on low until fully combined.
Increase mixer speed to high and beat for one minute, until smooth and fluffy. If frosting is too thick, add milk, 1 Tablespoon at a time until desired consistency is reached.
Divide frosting in half and add red food coloring to one half until desired shade of red is reached.
Place frosting in two piping bags fitted with a large round piping tip or large re-sealable sandwich bags with the corner snipped off. Alternate red and white frosting on top of cupcakes.