Preheat oven to 350 degrees F. Line a baking sheet with baking sheet with parchment paper or silicone baking mats. Set aside
In a small pot, simmer cream, milk, sugar and salt until sugar completely dissolves, about 5 minutes. Remove pot from heat.
In a separate bowl, whisk egg yolks.
Whisking constantly, slowly whisk about a third of the hot cream into the yolks, then whisk the yolk mixture back into the pot with the cream.
Return pot to medium-low heat and gently cook until mixture is thick enough to coat the back of a spoon (about 170 degrees on an instant-read thermometer).
Strain through a into a bowl and set aside to cool for a few minutes.
Spread the marshmallows out on prepared baking sheet. Place marshmallows in oven for 5 minutes.
At this point, you can either use the broiler or a kitchen torch to toast the marshmallow.
If you use a broiler, place the oven rack as high as possible and watch the very closely to ensure they don't burn. This should take about 2-3 minutes at most.
If using a kitchen torch, toast the tops and sides of the marshmallows, then rotate so that they are evenly toasted on each side.
In a blender, add the ice cream base and the toasted marshmallows and puree until smooth.
Place in a clean bowl, cover and chill completely in the fridge, at least 4 hours or overnight, until completely cool.
Once ice cream base is completely cool, churn in an ice cream maker according to manufacturer’s instructions.
While the ice cream is churning, chop the chocolate bars in bite-sized pieces and crush the graham crackers into small pieces. You can do this by placing the graham crackers in a sealed tiptop bag then rolling over them with a rolling pin or you can pulse in a food processor a couple of times. You want pieces of graham cracker, not crumbs.
Once ice cream has finished churning, pour half into an 8x8-inch baking pan lined with parchment paper or wax paper.
Sprinkle half the graham cracker crumbs and half the chocolate over top.
Repeat with remaining ice cream, graham crackers, and chocolate.
Serve directly from the machine for soft serve, or store in freezer until hardened.