Preheat oven to 325°. Line a 9x9 baking pan with parchment paper, set aside.
Prepare graham cracker crust by combining graham cracker crumbs, brown sugar and melted butter and stir very well to distribute all ingredients evenly. Press the mixture very firmly on the bottom of prepared baking pan, set aside.
Place butter, cocoa and sugar in a large microwave-safe bowl and microwave for about 1 minute and 30 seconds, or until butter is melted. Mix everything together until smooth. Add in eggs and vanilla and mix until smooth. Pour in the flour and mix until just combined. Then, mix some more until smooth and somewhat glossy. The batter will be very thick.
Pour the batter on top of graham cracker crust and smooth it out until level. Bake for 25-28 minutes or until a toothpick comes out slightly moist with a few crumbs on it. While brownies are baking take candy bars out of packaging and cut marshmallows in half because you will need to work quickly. Once brownies are done, pull them out of the oven and switch the oven to broil. Place candy bars in a single layer on top of the hot brownies. Break the 5th candy bar to fit around the edges. Line marshmallow halves on top of the candy bar. Place pan back in the oven under the broiler just to brown the marshmallows. Watch carefully because this only takes 30 seconds - 1 minute. Once marshmallows are browned, let the brownies cool for about 20 minutes before cutting into them. I like to stick mine in the fridge for an hour to really let the chocolate set up, then I let them sit out at room temperature. The easiest way to cut them is to spray non-stick spray onto the knife each time you slice through or else the marshmallow will be too sticky and unmanageable.
Brownies will stay fresh and marshmallows will stay soft for up to 3-4 days stored in an airtight container in the refrigerator or at room temperature. If storing in the refrigerator, take them out 1 hour before serving to let them come to room temperature.