In a medium bowl, combine graham cracker crumbs, cocoa powder, granulated sugar, and melted butter. Mix until well combined and crumbly.
Press half of the crumb mixture into the bottom of a 9x9-inch baking dish to form a crust.
Spread the vanilla ice cream evenly over the crust, smoothing it out with a spatula.
Sprinkle mini marshmallows and chocolate chips over the ice cream layer.
Top with the remaining crumb mixture, pressing it down gently to create a top layer.
Drizzle chocolate syrup over the top and cover the dish with plastic wrap.
Freeze for at least 4 hours or until firm.
Before serving, let the dish sit at room temperature for about 10 minutes for easier slicing. Cut into squares and serve with whipped cream on the side.