Bake the graham cracker pie crust about 10 - 15 minutes. Take out and allow to cool completely.
While the crust is baking, roast your marshmallows using a kitchen torch, getting as many of the sides as possible and getting them nice and burnt. Allow to cool completely.
Place the crust (minus the container it is in) into a large saucepan and add all the milk except 2 tablespoons. Simmer on medium-low for about 20 minutes. Add the heavy cream and stir well.
Strain the mixture through a fine mesh strainer lined with cheesecloth. Press down on the mixture to get as much of the milk and cream out as possible. It's okay if some of the graham cracker remains end up in the mixture, but keep it to a minimum or else the ice cream will be grainy.
Turn up the heat to medium. Add the sugar and corn syrup and mix well.
Take the remaining milk and add it to the cornstarch and mix well to create a slurry. Mix the cream cheese with the salt.
Add both the slurry and salted cream cheese into the milk mixture and mix well. Heat, stirring constantly, until the mixture becomes nice and thickened. The final mixture will be thicker than your typical ice cream base.
Place the ice cream base into a gallon freezer bag and store in the refrigerator until it is very cold, at least 40F. I usually leave mine overnight.
While it is chillding, mix together your chocolate and cream and heat on medium and stir until the chocolate is completely melted and combined well with the heavy cream. Set aside to cool.
Churn according to your ice cream maker's instructions (read my guice on how to make ice cream without an ice cream maker here). Add a thin layer of ice cream on the bottom of your ice cream container. Add a swirl of chocolate and then the roasted marshmallow. Continue layering the ice cream with the chocolate and the marshmallows until you run out of everything.
Freeze until firm, at least 3- 4 hours.
Notes
*I highly recommend using dark or semi-sweet chocolate. Even if you are not a fan of darker chocolate. The ice cream base is quite sweet, so the contrast of the darker chocolate works better than a sweet milk chocolate.