• Prepare an ice bath by placing a medium bowl over a larger container filled with ice water. Set aside.
• Arrange the marshmallows in a single layer on a parchment-lined baking sheet. Place under a broiler and toast for 30 seconds to 1 minute, watching carefully to prevent burning. Using tongs, turn the marshmallows and toast the opposite side. Remove from the oven and set aside.
• In a large, heavy-bottomed saucepan, combine the milk, cream, and one portion of the sugar. Heat over medium-high heat, stirring occasionally, until the mixture is hot and steaming, approximately 175°F.
• In a separate bowl, whisk the egg yolks with the remaining sugar until smooth. Gradually whisk approximately 1 cup of the hot milk mixture into the yolks to temper them. Slowly pour the tempered yolk mixture back into the saucepan, whisking continuously.
• Continue cooking the custard over medium heat until it reaches 180–185°F and thickens slightly. Do not allow the mixture to boil. Immediately transfer the custard to the prepared bowl set over the ice bath. Cool for approximately 15 minutes, stirring occasionally. Remove from the ice bath and stir in the vanilla extract.
• Place the toasted marshmallows in a blender. Add the cooled custard and blend until completely smooth, approximately 2 minutes. Transfer the mixture to a clean bowl, cover tightly with plastic wrap, and refrigerate until thoroughly chilled, at least 4 hours and up to 24 hours.

To Prepare the Fudge Swirl

• In a medium saucepan over medium heat, whisk together the sugar, water, corn syrup, and cocoa powder until the mixture begins to bubble around the edges. Bring to a gentle boil and cook for 1 minute, whisking frequently. Remove from heat, stir in the vanilla extract, and allow to cool. Refrigerate for at least 2 hours before use.

To Churn the Ice Cream

• Before churning, whisk the chilled custard until smooth and pourable. Transfer the mixture to an ice cream maker and churn according to the manufacturer’s instructions. When churning is complete, gently fold in the chopped graham crackers.
• Spoon a small amount of the fudge swirl into the bottom of a freezer-safe storage container. Layer the ice cream with additional spoonfuls of fudge swirl, finishing with a layer of ice cream. Do not stir. Cover and freeze until firm, at least 2 hours, before serving.