In a small bowl, stir together graham cracker crumbs and melted butter. Press evenly into the bottom of a 9x13 dish.
Using a mixer with whisk attachment on medium-low speed, beat ice cream and pudding mix until well incorporated, about 2 minutes.
Pour ice cream mixture over graham cracker crumbs.
Again, using a mixer with whisk attachment on medium-low speed, beat whipped topping, marshmallow creme, and vanilla extract until well combined, about 2-3 minutes. Spread evenly over ice cream mixture.
Break graham cracker squares into small pieces and sprinkle over top of dessert. Place in refrigerator for at least 2 hours before serving.