Combine the milk, sugar, 1 cup of the cream, and the salt in a medium saucepan. Scrape the seeds from the vanilla bean into the pan and drop in the vanilla pod and cinnamon stick. Heat over medium-high, stirring occasionally, until the mixture is warmed through. Remove the pan from the heat, cover, and let the mixture steep for 30 minutes.
Pour the remaining cup of cream into a bowl and set a fine mesh sieve over the top. In a separate medium bowl, whisk the egg yolks until smooth. Slowly pour the warm milk mixture into the bowl with the egg yolks, whisking constantly. Return the entire mixture to the saucepan and place over medium heat. Cook, stirring constantly and scraping the bottom of the pan, until the mixture thickens slightly and coats the back of a spoon (about 170˚-175˚ F). Pour the custard through the mesh strainer into the bowl with the cream. Stir in the vanilla. Let cool slightly, then cover and refrigerate until completely chilled.
Before you churn the ice cream, prepare the apples. Melt the butter in a skillet over medium heat. Add in the apples, sugar and cinnamon. Stir to coat well. Continue to cook, stirring frequently, until the apples have become golden brown and have cooked down a bit, about 12-15 minutes. Remove the pan from the heat, add the rum (if using), and cook once more until the liquid has burned off. Remove from the heat and let cool. Refrigerate briefly before adding to the ice cream.
Remove the vanilla bean and cinnamon stick from the ice cream batter before churning. Freeze in an ice cream maker according to the manufacturer’s instructions. Once the ice cream is churned, add half of it to a storage container with half of the apple slices and half of the graham crackers. Stir gently to combine. Add in the remaining ice cream, apples and graham crackers, and stir once more until well combined. Cover and freeze.