In a large mixing bowl, cream together 1 cup of unsalted butter and 8 oz. of cream cheese until smooth and fluffy, about 3 minutes. Gradually mix in 1 cup of granulated sugar, followed by 1 egg, 1 tsp of vanilla extract, and 1/2 tsp of peppermint extract.

Sift in 2 1/2 cups of all-purpose flour, 2 tsp of baking powder, 1/2 tsp of salt, and 1/4 tsp of baking soda to create a cohesive dough.

Divide the dough into two equal portions. In one half, add 1/4 cup of unsweetened cocoa powder, mixing until fully incorporated. In the other half, add food coloring as desired.

Roll the chocolate dough into a 9-inch square on parchment paper, then repeat with the colored dough. Stack the chocolate square on top of the colored one and roll them together jelly-roll style.

Wrap the log tightly in plastic wrap or parchment paper, refrigerating for at least 2 hours or until firm.

Preheat the oven to 350°F (175°C). Remove the chilled dough and slice it into 1/4-inch thick cookies. Place slices on a baking sheet lined with parchment paper.

Bake for about 12-15 minutes, or until the edges are lightly browned but centers remain soft. Let them cool on a wire rack.