First, Make The Cookie Dough:

1. Melt & Cool Butter. In a microwave-safe bowl, gently melt the butter in 15-20 second increments until smooth and fully melted. (You can also do this in a saucepan on low heat on the stove.) Cool the butter slightly so it’s not hot to the touch. You want it just barely warm or close to room temperature. 
2. Combine Wet Ingredients. When the butter has cooled, add it to the bowl of a stand mixer (or a large mixing bowl), along with brown sugar and sugar. Mix with a paddle attachment or handheld mixer on medium speed to combine Mix in egg and vanilla until the mixture is smooth and well blended. 
3. Add Dry Ingredients. Next, scrape down the sides of the bowl and add gluten-free flour, cocoa powder, and salt. Stir until the flour mixture is just fully incorporated and there are no floury or dry patches left in the dough. (The dough will look like thick, sticky brownie batter.) 
4. Chill 30 Minutes. Cover the dough and chill in the refrigerator 3o minutes. (I recommend just 30 minutes–see notes below for more info!)

Next, Stuff & Bake The Cookies:

1. Preheat Oven & Prep Pan. While the cookie dough chills, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
2. Cut Marshmallows In Half. When you’re ready to bake the cookies, cut 3 marshmallows in half width-wise. (The short way, not the long way)
3. Scoop Dough & Stuff With Marshmallows. Use a medium cookie scoop to measure six (2-Tablespoon) cookie dough balls. Use your fingers to pat out a cookie dough ball into a flattened disc, about 3-inches wide. Add a marshmallow half to the center, then fold up the sides of the dough disc to cover the marshmallow & roll the cookie dough ball so it’s smooth and the marshmallow is well covered. (If desired, you can leave one very small opening at the top for the marshmallow to escape from–see notes.) Repeat until you have 6 stuffed cookie dough balls. Return the rest of the cookie dough to the fridge while you bake these 6 cookies. 
4. Bake & Shape Cookies. Place stuffed cookie dough balls on a prepared baking sheet and bake at 350 degrees for 9-10 minutes. The edges of the cookie should look set and the marshmallow should have created a crackle in the center to bubble through. Use a large round cookie cutter to gently shape the cookies into perfect circles while they’re hot from the oven. 
5. Cool & Repeat. Let the cookies cool 3-5 minutes on the baking sheet before using a spatula to transfer them to a wire rack to cool completely. Repeat baking process, stuffing and rolling cookies, baking, and cooling, until all the cookies are baked. (The last batch will likely only have 4-5 cookies)
6. Serve & Store. Enjoy the cookies right away, or store in an airtight container at room temperature 2-3 days. Or, store cooled cookies in a freezer bag and transfer to the freezer up to 2 months.