Preheat the oven to 350F (180C or 160C fan forced). Position the oven rack in the middle of the oven.
Line 2 baking sheets with parchment paper or silicone baking mats.
Whisk together the flour, cocoa, cornstarch, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat together the cold butter, brown sugar, granulated sugar and orange zest. Cutting the butter into chunks first will make this easier.
With the mixer on a low speed, beat the flour mixture into the butter mixture. I often do a few stirs by hand first.
Stir the chopped chocolate into the dough.
Form the dough into balls. For large cookies (like the ones pictured) form the dough into balls with about 3 tablespoons of dough each (you'll get about 15 cookies). For smaller cookies, form the dough into balls with about 1 to 1.5 tablespoons of dough (you'll get about 30 cookies)
Place the dough balls 2 inches apart on the lined cookie sheets. If it feels very sticky, pop the dough in the fridge for 15-30 minutes before baking.
Bake 1 sheet at a time in the middle of the oven for 11-13 minutes for large cookies, or 8-10 minutes for small cookies. When the cookies come out of the oven, optionally place an additional segment of chocolate orange on top of each cookie.
Cool on the cookie sheets for at least 10 minutes, then transfer to a cookie sheet to continue cooling.