Start by preheating the oven to 350 degrees Fahrenheit and line 3 standard baking trays with parchment paper for later.
Then in a large mixing bowl combine softened butter and peanut butter using a hand mixer until smooth.
Now throw in the brown sugar and cane sugar and beat until fluffy about 1-2 minutes.
Add in the eggs and vanilla extract and mix until combined.
In a smaller mixing bowl mix all dry ingredients (flour, baking soda, baking powder and salt) together with a fork.
Pour the dry ingredients into the wet ingredients and fold the two into each other using a rubber spatula; stop mixing the moment the last bit of flour disappears.
Set the dough aside.
Place 5 half graham cracker sheets onto one of the baking trays lined with parchment paper.
With a large cookie scoop (about 3 oz) scoop the dough onto the top of each cracker.
Using a fork cross smash the cookie dough down in each direction.
Bake the cookies for 8 minutes in the preheated oven at 350 degrees Fahrenheit.
After 8 minutes of baking, press the centers of each cookie with half of a large marshmallow.
Bake the cookies for 4 more minutes before removing them from the oven to cool.
Continue baking the cookie dough until all the cookies are baked.
Now prepare the frosting.
In a small saucepan over medium heat melt the butter and then stir in the cocoa powder with a whisk until combined.
Remove the saucepan from the heat and stir in 1 cup of powdered sugar and 2 tablespoons of milk until smooth.
Repeat and add another cup of powdered sugar and 2 tablespoons of milk.
Once the frosting is silky and fudgy drizzle the tops of the cookies, making sure to cover the marshmallow.
Serve and enjoy.
Store leftover in an airtight container at room temperature out of the sun for up to 3-5 days.