Preheat the grill to 325°F and brush the grill grates clean.
Use a mixer fitted with a paddle attachment to mix the butter and sugar together for 3 minutes on medium speed, scraping down the sides of the bowl as needed.
Add the vanilla extract to the butter mixture. With the mixture running, add the eggs, one at a time, making sure the egg is fully incorporated before each addition. Scrape the sides of the bowl again, making sure to scrap the bottom of the bowl as well.
Mix the flour, graham cracker crumbs, baking powder, and salt together in a separate bowl.
Add the dry ingredients to the wet ingredients and mix on medium speed until just combined, then stir in the first amount of chocolate chips.
Prepare a 9 x 13 baking dish by rubbing it with the melted butter.
Transfer batter to the pan, pressing the batter down or using a spatula to spread it evenly across the pan.
Sprinkle the batter with the second amount of chocolate chips.
Put the marshmallow cream into a pastry bag (or zip-top bag with one corner cut to make a piping bag) and pipe diagonal lines onto the top of the batter.
Place baking dish on the top shelf of the grill and bake, rotating halfway through, until a toothpick inserted into the batter comes out clean, about 30 minutes.
Remove the pan from the grill and allow it to cool, before cutting into squares and serving.
