In a small pot, heat the heavy cream, butter and sugar over a medium heat, stirring frequently until the butter is melted and the sugar is dissolved. Bring to a boil, stirring constantly, then reduce heat to medium-low and boil for 2 minutes.
Remove the pot from the heat and stir in the chocolate and a pinch of salt, stirring well until the chocolate is fully melted and the mixture is smooth. Pour into a bowl or baking tin and let cool in the fridge while you make the ice cream.
Spread your marshmallow fluff on a parchment covered baking pan, about a half inch thick or as thin as you can. Use your chefs torch to roast the marshmallow. Alternatively, you can use your oven and use the broil option.
In your stand mixer, whip the cold heavy whipping cream until soft peaks form. Turn the mixer on high speed and continue to whip, adding the sweetened condensed milk in a steady stream until it's fully incorporated and the mixture almost reaches the hard-peak stage. Mix in the vanilla and a pinch of salt. Set aside once hard peaks form.
Remove the chocolate sauce from the fridge--it should no longer be warm. Spread half of the ice cream base into your baking pan. Drizzle with half of the chocolate sauce, then dollop half of the roasted marshmallow fluff over the top. Use a skewer to gently swirl the mixture to combine. Crumble 3 of the graham crackers over the top.
Pour the remaining ice cream base on top, and repeat the process above with the remaining chocolate sauce, marshmallow fluff and graham crackers. Top with marshmallows and roast with your torch.
Wrap the pan tightly in plastic wrap and freeze until firm, at least 4 hours. Serve or keep frozen for up to 2 weeks, tightly wrapped in plastic.