Place the marshmallows on a cookie sheet lined with parchment paper. Place on lower rack of oven, and broil marshmallows until nice and brown on top, between 30 to 60 seconds. Remove pan from oven and gently turn the marshmallows over, and broil until they are golden brown. (Be sure to keep an eye on them because they burn very quickly.)
Combine the ice cream, milk, and yogurt in a blender; blend well. Add the marshmallows and blend until they are broken up and distributed evenly.
Pour the shake into two glasses and top with graham cracker crumbs and shaved chocolate, as desired.
You can double the recipe for double the servings.
Use gluten free graham crackers or cookies to make it gluten free.