For the fudge sauce: In a small pot, heat the heavy cream, butter and sugar over 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 an 8- or 9-inch cake pan and keep in the freezer while you prepare the ice cream (see Cook's Note).
For the ice cream: Whip the heavy cream with an electric mixer on medium-high speed in a large bowl to medium peaks. With the mixer running, add the sweetened condensed milk in a slow, steady stream. Mix in the vanilla and a pinch of salt. Set aside.
Scoop the marshmallow creme into a disposable pastry bag or resealable plastic bag and cut a 1/2 inch opening from the tip. (This makes it easier to create streaks and swirls of marshmallow in the ice cream. Alternatively, you can just dollop the marshmallow creme over the ice cream, but it will be less streaky and more like mounds of marshmallow throughout). Remove the fudge sauce from the freezer--it should no longer be warm.
Pour half of the ice cream base into a 9-by-9-inch baking pan. Drizzle with half of the fudge sauce, then squeeze half of the marshmallow creme 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 fudge sauce, marshmallow creme and graham crackers.
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 to avoid freezer burn.
The fudge sauce can be made up to 4 days ahead and stored in an airtight container in the refrigerator. Bring to room temperature before using to soften slightly.