Chop the mini marshmallows in half. Chop the graham crackers into pieces. Set aside.
In a mixing bowl combine cream vegan butter until light and fluffy. Add the sugars and beat on medium speed until light and fluffy, around 2 minutes. Add the vanilla. Mix again until well incorporated. Set aside.
In a medium-size bowl, combine the flour, cornstarch, baking soda, baking powder, and salt. Stir to combine. Pour the flour mixture over the butter mixture and mix to combine.
Reserve some of the marshmallows. Then add the chocolate chips, chopped graham crackers, and remaining marshmallows into the cookie dough batter. Stir to combine. Refrigerate the batter for 30 minutes to an hour.
Preheat oven to 350°F/177°C.
Keep a mister nearby to lightly mist the dough if necessary. This dough is a little bit dry when chilled, but it creates the best cookies.
Use a cookie dough dispenser to drop rounded spoonfuls of cookie dough onto an ungreased cookie sheet, roughly 2" apart. Bake for 8 minutes, then remove and add reserved chopped marshmallows and some chopped graham cracker pieces. Return to the oven and bake for 2 more minutes, until the edges are golden brown, but cookies are still soft.
Remove from the oven and use a butter knife to fix any messy marshmallows or chocolate on the cookies. Allow the cookies to cool slightly before transferring to a wire rack to cool completely. Then add a piece of chocolate bar to the center. Repeat with the remaining dough.
Freezer tips: Roll the entire batch into cookie dough balls, place them on a tray and put that tray in the freezer. Wait about 15 minutes and then transfer those cookie dough balls to a freezer bag.
Baked cookies should be stored in an airtight container for up to 4 days at room temperature, for one week in the fridge, and up to 2 months in the freezer.