In the bowl of a stand mixer with the paddle attachment, cream the butter and sugars until fully mixed and fluffy. Add in the egg and yolk, beating until combined, then add the vanilla extract.
In a separate bowl, mix together the flour, baking soda, and salt, then add into the wet mixture and beat until just combined.
Gently fold in chopped chocolate and crushed graham crackers until evenly dispersed through the cookie dough.
Use a cookie scoop to evenly form 12-14 balls of dough. Press your thumbs into the center of each ball to form a divot, then add a marshmallow half in the centers. Shape the dough up and around the marshmallows until they're covered by the dough ball. If you want the marshmallows to peek through when baked, leave a small hole at the top of each dough ball so you can see the marshmallows inside.
Chill in the fridge for at least 1 hour or covered overnight. Dough should be very firm before baking.
Preheat the oven to 350ºF and prepare a baking sheet with parchment paper.
Bake cookies for 12-15 minutes, until the edges have become golden and the marshmallows have melted.
Use a large cup or round cookie cutter to scoot the cookies into even circles, then let them rest at room temperature for at least 5 minutes to finish baking before serving.