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Remove ice cream from freezer and let it melt and come to room temperature.
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Preheat the oven to 350 degrees F. Butter the bottom and sides of a large Springform pan.
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Add butter to a medium heatproof mixing bowl. Microwave for 30-60 seconds until melted. Mix in the graham crackers, brown sugar, salt, and cinnamon using a rubber spatula. Mix until butter coats each little graham cracker crumb.
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Add the graham cracker mixture to the Springform and press into one even layer along the bottom of the pan. Bake the crust for 12-15 minutes until golden. Let the crust cool while the ice cream melts.
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Chop the milk chocolate and graham crackers into small pieces. If you feel like doing some extra work, torch or roast the mini marshmallows over an open flame until they turn golden brown.
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Once the ice cream is melted and easily workable, add it to a large mixing bowl. Mix in the chopped chocolate, chopped graham crackers, and mini marshmallows. Be sure to save some of the chocolate, graham crackers, and toasted marshmallows for the top of the cake.
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Drizzle the top of the cake with the chocolate magic shell or chocolate sauce. Add the remaining toppings and freeze the cake overnight.