Preheat the oven to 350 degrees F. Spray a 9×13-inch baking dish with nonstick spray. In a small bowl, whisk together the flour, graham crumbs,, baking powder and salt.
In the bowl of your electric mixer, beat the butter until creamy. Add the sugars and beat until fluffy, about 2 to 3 minutes. Add in the egg and beat for another minute or so until combined, scraping down the sides of the bowl if needed. Beat in the vanilla extract.
With the mixer on low speed, gradually add the dry ingredients until combined. Scrape the sides if needed. Once the dough has come together, stir the chocolate chips and 3/4 of the marshmallows into the dough with a spatula.
Press the mixture into the greased baking dish. Top if with the leftover marshmallows, the chopped chocolate and the graham pieces. Bake for 20 to 25 minutes. Let cool and set completely before serving.