First, Brown the Butter. Melt the butter in a light-colored saucepan over medium heat, whisking constantly until the butter begins to foam. (Watch carefully when the butter begins to foam, as it will turn golden and brown quickly.) When the butter under the foam is golden (like honey) and smells sweet, remove the pan from the heat and transfer to the bowl of your stand mixer or a mixing bowl to cool to room temperature.
Cool, Then Add Sugars. When the butter has cooled, add the sugar and brown sugar. Mix 2-3 minutes or until well combined and the mixture looks like wet sand.
Finish Wet Ingredients. Add eggs + egg yolk one at a time, blending well after each addition. Then, Add the vanilla and mix to combine.
Add Dry Ingredients, Then Mix-Ins. Add gluten-free flour, cornstarch, baking powder, baking soda, and salt. Mix until mostly combined, with just a few floury patches left. Add 1 1/2 cups chocolate chips and 3/4 cup graham cracker pieces and stir to combine until evenly blended.
Scoop & Chill The Dough. Use a large cookie scoop (3 Tablespoon size) to scoop cookie dough balls. Place in an airtight container, cover, and chill the cookie dough balls for at least 2 hours.
Preheat The Oven & Prep Your Pans. When you’re ready to bake, preheat oven to 350 degrees F. Line two baking sheets with parchment (so you can alternate sheets between batches.)
Roll & Bake The Cookies. Working with just 6 cookie dough balls per batch, flatten each dough ball out into a disc. Add a marshmallow half to the center of the disc, and fold the dough around it, leaving a small opening at the top of the cookie for the marshmallow to expand through during baking. Make sure the dough is sealed well around the sides and bottom of the cookie dough ball! Place cookie dough balls on a prepared baking sheet and bake cookies at 350 degrees for 10-12 minutes, or until the edges are a golden brown color and the centers look just underdone.
Garnish & Finish Cookies. Garnish cookies right away with a few extra chocolate chips, some extra graham cracker crumbs, and a square of Hershey's chocolate. Let the cookies cool 1-2 minutes on the baking sheet before transferring to a wire rack to finish cooling completely. Repeat process with remaining cookie dough until all cookies are baked and cooled.
Serve & Store. Enjoy right away once the cookies are cooled down, or store in an airtight container 2-3 days. (Or, freeze up to 2 months)