Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream butter and sugar for 2–3 minutes until light and fluffy.
Beat in egg and vanilla until smooth.
In a separate bowl, whisk flour, baking powder, and salt.
Add dry ingredients to wet ingredients and mix just until combined.
Divide dough evenly into two bowls.
Mix cocoa powder into one bowl (chocolate dough).
Mix peppermint extract and food coloring (if using) into the other bowl (mint dough).
Shape each dough into a rectangular log, wrap in plastic wrap, and chill 30–45 minutes.
Slice each log lengthwise into equal strips.
Alternate chocolate and mint strips to form a checkerboard pattern.
Gently press together, reshape into a log, and chill 15 minutes.
Slice into ¼-inch cookies and place on baking sheets.
Bake for 10–12 minutes, until edges are set.
Cool on the pan for 5 minutes, then transfer to a wire rack.