In a medium bowl, whisk together the gluten-free flour, cornstarch, cocoa powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer, cream together the softened butter and light brown sugar on medium speed until light and fluffy, about 4-5 minutes.
Add the vanilla extract to the butter mixture and mix until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Increase speed to medium and beat until the dough comes together.
Mix in the dark chocolate pieces on low speed until evenly distributed.
Divide the dough in half and roll each portion into logs approximately 1.5 inches in diameter. Wrap in parchment paper and refrigerate for 2 hours or up to 3 days.
Preheat your oven to 325°F (160°C) and line baking sheets with parchment paper.
Remove one dough log at a time from the fridge and slice into discs approximately 0.5 inch thick. Arrange on baking sheets, 2 inches apart.
Bake for 10-12 minutes until cookies appear set around the edges. Let cool completely on baking sheets.
Notes
Store cookies in an airtight container at room temperature for up to 5 days. For a vegan option, use a firm vegan butter.