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1
Preheat broiler to high and adjust rack to 6-inches below element. Evenly distribute marshmallows in a wide broiler-proof baking dish. Broil until tops of marshmallows are toasted brown, about 4 minutes. Remove from broiler and stir marshmallows into a paste, making sure to incorporate toasted top into paste.
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2
Return to broiler until top is toasted brown, about 2 minutes. Remove from broiler and stir paste again to incorporate toasted top. Repeat until marshmallow paste is an even, tan color, 4 to 5 times total. Remove from broiler and set aside.
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3
In a heavy saucepan, whisk together egg yolks and sugar until well combined. Slowly whisk in milk, stirring well to fully incorporate yolk mixture. Whisk in cream.
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4
Using a spatula, transfer toasted marshmallow paste to saucepan and place over medium heat. If paste seizes up, stir frequently with whisk to break up marshmallow chunks. As custard base heats the paste will dissolve.
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5
Cook until the custard thickens and coats the back of a spoon; a swiped finger on the spoon should leave a clean line. Add vanilla and salt to taste, then strain into an airtight container and chill overnight before churning according to manufacturer's instructions. Chill ice cream in freezer for at least three hours before serving,
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6
Place a heavy saucepan over low heat and melt chocolate and butter together with corn syrup and sugar. When fully combined, whisk in cocoa powder until no lumps remain. Whisk in water, salt, and vanilla and cook until sauce just reaches a simmer. Sauce can be served immediately or refrigerated for later. To warm up again, microwave sauce for 30 to 60 seconds.
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7
Scoop ice cream over graham crackers and top with hot fudge sauce.
