Preheat the oven to 375°F. Line two baking sheets with silicone baking mats or parchment paper.
In a stand mixer with a whisk attachment, cream together the butter and sugars for 1 minute. Add the eggs and vanilla and mix until combined.
Switch the stand mixer to a paddle attachment. Add the flour, baking soda and salt and mix just until combined.
Add the mini marshmallows, chopped chocolate, and crumbled graham crackers to the dough, while reserving about a 1/2 cup of marshmallows and chocolate chunks for topping. Give a quick mix, careful not to overbeat.
Using a cookie scoop or ice cream scoop (about 1-1/2 Tablespoons), scoop the cookie dough onto the baking sheet about 2 inches apart.
Bake for 5 minutes until cookies are just about set. Remove from the oven and top with additional mini-marshmallows and chocolate chunks. Return to the oven for 3-4 minutes for the cookies to finish baking and marshmallows start to puff.
Allow cookies to cool on pan for 2 minutes, and then transfer to a wire cooling rack.
The standard mini-marshmallows work perfectly for this. If you have only large marshmallows, do not add any to the batter, simply squish only one into the center of the cookie after the initial 5 minutes of baking. If that seems like too much marshmallow for you, chop the large marshmallows in half before placing on the cookies.