Melt the butter so it is 90% melted (not all of the way) in the microwave. Whisk in the white sugar and brown sugar until completely combined.
Add in 1 full egg and then 1 egg yolk (discard the whites or save for another recipe). Whisk in the vanilla.
In another bowl, toss together the flour, baking soda, and salt. Add full graham crackers to a blender or food processor and crush until you have 3/4 cup of very fine crumbs (not packed in the measuring cup; just loosely measured). Add in the milk chocolate chips and miniature chocolate chips. Stir.
Combine the wet and dry ingredients and mix until JUST combined avoiding over-mixing.
Cover the bowl tightly and chill the dough for 1 hour and up to 8 hours.
Preheat the oven to 350 degrees F and line a pan with parchment paper or a silpat liner.
Form large and tall (rather than wide) balls of cookie dough and space 6 per large cookie sheet (to allow PLENTY of room for spread). You should get 14-16 cookies from this dough.
Place the cookies in the oven and bake for 9 minutes. Meanwhile, coarsely chop the Hershey's bars.
Remove the cookies and press 3-4 miniature marshmallows and 3-4 chunks of Hershey's chopped chocolate on to each cookie. Return to the oven for an additional 1-3 minutes.
Remove from the oven and allow to cool.