Make the Ice Cream Base: Spread the marshmallows in a single layer on a parchment-lined baking sheet. Place them under the broiler for 30 seconds to 1 minute, or until toasted. Flip them over and pop them back under the broiler for another 30 seconds. Set the marshmallows aside.
Place the milk in a medium saucepan. Split the vanilla bean down the middle and scrape the seeds into the pan with the milk. Set the pan over medium heat and bring the mixture to a simmer.
Meanwhile, whisk together the egg yolks, granulated sugar, and salt in a large, heatproof bowl. Slowly add the warm milk mixture to the egg mixture, whisking constantly. Pour the mixture back into the saucepan, scraping it back into the pan. Turn the heat down to medium-low and cook until it thickens enough to coat the back of a spoon. Strain through a fine-mesh sieve into a heatproof bowl.
Let the mixture cool for about 15 minutes, stirring every few minutes. Blend the toasted marshmallows and the custard until smooth. Add the heavy cream and vanilla extract, blending to combine. Refrigerate overnight.
For the Fudge Swirl: Whisk together the granulated sugar, water, corn syrup, and cocoa powder in a medium saucepan. Cook until it bubbles, whisking constantly, and then boil for 1 minute. Remove from heat and stir in vanilla. Cool and chill for at least 2 hours.
Churn the ice cream: Whisk the custard until smooth before churning. Freeze in the ice cream maker as per manufacturer's directions. Once done, fold in the chopped graham crackers.
Layer the fudge swirl: Spoon some fudge swirl into a container, alternating with layers of ice cream. Freeze until firm.
