Preheat oven to 350 degrees F. Line a baking sheet with parchment paper. Set aside.
In a medium-sized bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and corn starch and salt. Set aside.
In a stand size mixer fitted with the paddle attachment, cream the softened butter and both sugars on medium speed until light and fluffy, about 2-3 minutes.
With a rubber spatula, scrape down the sides and bottom of the bowl. Add the egg, mix on medium speed for 20 seconds, scrape down the sides, add the egg yolk, and mix for 20 more seconds. Add the vanilla and peppermint extracts and mix on low until just combined.
Add the chocolate chips and peppermint to the bowl. Then, add the dry ingredients mixture. Mix on low until just combined. Be cautious not to overmix; stop as soon as there are no more flour streaks.
Using a 3-tablespoon scoop, portion out the dough onto the prepared sheet pan, spacing them about 3 inches apart. Bake for 8-10 minutes, checking for doneness at the 8-minute mark. Let the cookies cool on the baking sheet for a few minutes before transferring to a cooling rack to finish cooling.
While the cookies are cooling, melt the dark chocolate using a microwave or double boiler. You can either drizzle the chocolate on top of the cookies with a piping bag or dip half of each cookie and garnish with extra peppermint.