Preheat your oven to 375 degrees F and with a hand mixer, beat together the butter and sugars in a large mixing bowl. Beat in the eggs and vanilla extract until the mixture is smooth and combined.
Add in the baking soda, baking powder, flour, and graham crackers and gently stir into the mixture until there are no more clumps of dry flour remaining in the cookie dough.
Place balls of dough roughly the size of one tablespoon on an ungreased cookie sheet and use your thumb or the back of a teaspoon to make a small indent in the center of each cookie.
Bake the cookies for four minutes.
Remove the pan from the oven (you may need to press down the center again if needed) then place a few marshmallows in the center of each cookie and place them back in the oven for another four minutes.
Once the cookies are done baking, melt the chocolate chips in the microwave or over a double boiler and drizzle the chocolate over the cookies.
Allow the cookies to cool slightly before removing them from the pan. Serve and enjoy!