Preheat the oven to 350 F. Line an 8X8 baking dish with parchment paper.
Mix graham crackers and butter in a bowl, press in at the bottom of the baking dish using a measuring cup. Place the baking dish in the freezer for 10 minutes so it sets.
Melt the butter and chocolate in a microwave safe bowl for 1 minute and 30 seconds. Stir every 15 seconds to avoid burning.
Take the baking dish out of the freezer and let it sit on the counter.
Whisk in sugar, mix until well combined. Whisk in the eggs, one at a time, stir very well.
Stir in flour, mix slowly until fully combined.
Pour the brownie batter on top of the crust and bake in the oven for 30 - 35 minutes until toothpick inserted in the brownie comes out clean or with very few crumbs.
Take the brownies out of the oven and let it cool for 10 minutes. Turn the broil on. Top the brownies with marshmallows and place the dish in the oven until the marshmallows are perfectly toasted (about 2 to 4 minutes)
Let it cool a bit and then cut into desired pieces.