In a medium bowl, combine the flour, cocoa, powder, baking powder, cornstarch, and salt. Set aside.
In a large bowl, add the butter, cream cheese, and sugar. Use an electric hand mixer and beat on medium speed for 2-3 minutes until light and fluffy.
Mix in the egg, vanilla, and peppermint extract on high speed until well combined.
Add in the dry ingredients and mix on low speed until mostly combined. Use a rubber spatula to scrape down the bowl and finish mixing until all of the dry ingredients have been fully incorporated.
Wrap the cookie dough in plastic wrap and shape into a disk. Chill in the fridge for at least 2 hours or overnight.
When ready to bake the cookies, preheat the oven to 350 degrees F and line two baking sheets with parchment paper.
Roll the dough out to ¼" in thickness between two pieces of parchment paper dusted with cocoa powder or flour.
Cut out the cookies and place on the prepared baking sheets. Freeze the cutout cookies for at least 15 minutes. Re-roll the dough and cut out more cookies as needed.
Bake the frozen cookie dough for about 12 minutes. Allow them to cool completely on the baking sheet before dipping in chocolate.