Preheat the oven to 375°F.
While the oven is preheating, cream the butter and sugar in a large mixing bowl using an electric hand mixer on medium-high speed. You can also use a stand mixer if you have one. Mix the ingredients for 2-3 minutes, or until smooth.
Add the egg and vanilla. Mix the ingredients for an additional minute to fully incorporate the egg.
On a low speed, slowly incorporate the flour, graham cracker crumbs, baking powder, and baking soda until no pockets of dry ingredients remain in the cookie dough.
Drop dollops of dough about 1 ½ tablespoons in size on a baking sheet. Leave about an inch between each cookie and bake them for 11 minutes.
Once all the cookie dough has been baked, top half the cookies with 2 pieces of Hershey chocolate and one marshmallow. Broil the topped cookies on high for about a minute, or until the marshmallows are golden brown.
Remove the pan from the oven and top each s’more sandwich with the remaining cookies.
Serve immediately and enjoy!