Heat the oven to 350 degrees and line a small baking pan with parchment. Mix the crushed graham crackers with the melted butter, then press the mixture into the bottom of the pan to form a crust.
In a mixing bowl, melt the remaining 1/2 cup butter. Stir in the sugar until combined, then add the eggs one at a time. Mix in the cocoa powder, flour, and vanilla until the batter is smooth.
Pour the brownie batter over the graham cracker crust and spread it evenly. Bake for 20 minutes until the center is just set.
Remove the pan from the oven and sprinkle the mini marshmallows and chocolate chips over the top. Return the pan to the oven for 3 to 5 minutes until the marshmallows turn golden.
Let the brownies cool in the pan for 10 minutes before slicing into 4 pieces.