Preheat oven to 350°F. Line a 9×9 baking dish with parchment paper, leaving two sides higher to create a sling.
In a medium bowl, stir together graham cracker crumbs, melted butter, sugar, and vanilla until fully coated.
Line the bottom of the baking dish with whole graham crackers, breaking as needed to fit.
Spread half of the buttered crumbs over the graham crackers.
Sprinkle 1½ cups semi-sweet chocolate and 1½ cups milk chocolate chips over the crumbs.
Add 1½ cups mini marshmallows.
Add another layer of graham crackers.
Spread remaining buttered crumbs over the top.
Sprinkle remaining chocolate over the crumbs. Do not add the remaining marshmallows yet. Bake for 15 minutes.
Remove from oven and increase temperature to broil.
Sprinkle remaining mini marshmallows over the chocolate. Broil for 1–2 minutes, watching closely so they do not burn.
Cool for 20–25 minutes, then refrigerate for 1 hour to make slicing easier.
Lift out using the parchment paper sling.
Spray a sharp knife with nonstick cooking spray and slice into 16 squares.