In a large bowl, beat together the butter and sugar until light and fluffy, about 2 minutes.
Beat in the egg, vanilla extract and optional peppermint extract until combined.
In a small bowl, whisk together the flour, baking powder, cream of tartar and salt.
Beat the flour mixture into the butter mixture.
Divide dough in half and dye half red with the food dye.
On a clean floured surface, place small balls of each color of dough in a random pattern.
Use a floured rolling pin to roll the doughs together. You may want to fold and re-roll a couple times to get the marbled effect you desire.
Wrap the dough in plastic wrap and refrigerate 1 hour.
Preheat oven to 350F and remove the dough from the fridge.
Line or grease 2 cookie sheets.
Use cookie cutters to cut out your desired shapes and place on prepared cookie sheet.
Bake for 4-6 minutes, until lightly browned and set on the edges.
Allow cookies to cool completely before preparing the glaze.