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1
Prepare an ice water bath by filling a bowl halfway with ice and water; set it aside.
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2
Place a fine-mesh strainer over a large heatproof bowl; set it aside.
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3
Whisk together the cream, milk, cocoa powder, granulated sugar, vanilla, and salt in a medium saucepan.
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4
Heat the mixture over medium heat, stirring occasionally, until steam begins to rise from the surface, about 5 minutes.
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5
Meanwhile, whisk the brown sugar and egg yolks in a large bowl until smooth; set aside.
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6
While whisking constantly, slowly pour about half of the heated cream mixture into the egg yolks.
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7
Pour the cream-egg mixture back into the pan and cook over medium heat, stirring constantly with a wooden spoon or rubber spatula, until the mixture thickens slightly and coats the back of the spoon, or registers 170 degrees F on an instant-read thermometer, about 5 minutes (do not let the mixture boil).
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8
When you draw your finger across the spoon, it should make a mark through the custard, which should not run back in on itself.
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9
Pour the mixture through the prepared strainer into the bowl and discard the contents of the strainer.
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10
Place the bowl in the ice water bath and let the custard cool, stirring occasionally, until it reaches room temperature, about 20 minutes.
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11
Press a sheet of plastic wrap directly onto the surface of the custard to prevent a skin from forming.
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12
Refrigerate it until completely chilled, at least 4 hours.
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13
Freeze the chilled custard in an ice cream maker according to the manufacturers instructions.
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14
Meanwhile, place the chocolate in a small microwave-safe bowl and microwave it in 20-second intervals, stirring between intervals, until melted and smooth.
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15
When the ice cream is ready, turn off the ice cream maker and remove the bowl.
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16
Drop the marshmallow creme into the ice cream in large spoonfuls.
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17
Drizzle in the melted chocolate and add the graham crackers.
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18
Using a rubber spatula, fold the ingredients into the ice cream until evenly combined.
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19
Serve immediately for a soft ice cream, or transfer the mixture to an airtight container and freeze until solid.
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20
Allow the ice cream to sit at room temperature for 15 minutes before serving if frozen solid.
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21
The ice cream can be kept for up to 1 month.