Mix brown sugar and cocoa powder in a small bowl. Set aside.
In a medium saucepan, cook butter and milk until it starts to bubble ( about 5 min on medium heat).
Add cocoa mixture. Stirring constantly with a wooden spoon, cook for 2 minutes until smooth.
Remove from heat and stir in vanilla.
Let sit for at least 5 minutes. It will thicken.
Store covered in refrigerator for up to 1 week.
Reheat for 10 seconds in microwave before using.
!to make the ice cream:
In a large mixing bowl, whisk together half and half, cream, vanilla and powdered sugar. Chill in the fridge for 1 hour.
In the meantime, place the mini marshmallows on a parchment paper lined large baking sheet and toast under the broiler until nicely browned. Watch them because as soon as they start to brown they can burn quickly!
Let cool until safe to the touch.
Remove the marshmallows from the sheet into a measuring cup or small bowl. It's a little messy but a delicious task.
Get your ice cream maker ready.
Pour the cream mixture into the ice cream maker and turn it on.
As soon as you see that the mixture starts to freeze and thicken, add the marshmallows and graham cracker pieces. Finish churning.
Place the ice cream mixture in a container. Drizzle about 4 tablespoons of the fudge sauce over the top of the ice cream. Swirl with a spoon.