Move oven rack to the upper-middle position and preheat oven to 350 degrees F. Grease a mini muffin tin; set aside.
In a medium bowl add the graham cracker crumbs, flour, baking soda, and salt. Whisk together and set aside.
In a large bowl, or in the bowl of a stand mixer, add the butter and sugars. Mix on medium speed until creamy and smooth, about 2 minutes. Add the egg and vanilla and mix until combined. Add the dry ingredients and slowly mix to combine.
Fill the muffin tin wells 2/3 full with dough. Bake for 6-8 minutes, or until lightly golden. Switch oven broiler to medium. Add 1 chocolate piece to each cookie. Then top with a marshmallow. Place cookie bites under the oven broiler and watch carefully! Broil for 1-2 minutes, or until desired browning is reached.
Let cookie bites cool for 10 minutes before moving them to a wire rack. Cool for 20 more minutes before serving. Repeat with leftover cookie dough or freeze for later (see cook's note above).