Brown the butter in a saucepan over medium heat until golden brown, about 5-7 minutes. Remove from heat and cool slightly for 10 minutes.

Mix the cooled brown butter with granulated sugar and brown sugar until the mixture resembles wet sand.

Incorporate eggs and vanilla one at a time, beating well after each addition until smooth.

In another bowl, whisk together gluten-free flour, cornstarch, baking powder, baking soda, and salt. Gradually add to wet ingredients until just combined.

Fold in chocolate chips and crushed graham crackers until evenly distributed.

Scoop cookie dough into balls and chill in the refrigerator for at least 2 hours.

Preheat your oven to 350°F (175°C) and prepare baking sheets with parchment paper.

Flatten each dough ball slightly and place half a marshmallow in the center, wrapping the dough around it.

Bake cookies for 10-12 minutes until edges are golden brown and centers look slightly underbaked.

Immediately sprinkle additional chocolate chips and graham cracker bits on top while warm.