Preheat oven to 350°F and line three baking sheets with parchment paper.
Cream butter and light brown sugar on medium speed with a mixer until combined and fluffy. Add vanilla and eggs; mix until just combined.
Whisk together graham crumbs, flour, baking powder, cornstarch, and salt. Add half of flour mixture to the butter mixture. Mix on low speed until just combined, and then medium speed until completely combined. Repeat with second half of flour mixture.
Fold in chocolate chips, 1 ½ cups mallow bits, and graham crackers.
Using a cookie scoop (I used a 1 ½” scoop), scoop a ball of dough and use your thumb to press a hole into the center. Place cold mini marshmallows inside and fold dough around the marshmallows so that it wraps completely around the sides but leaves some of the marshmallows exposed in the middle of the ball of dough.
Arrange balls of dough 2-inches apart on the prepared baking sheets. (I fit about 8 on each sheet and reused the pans a couple of times.)
Press additional chocolate chips, mallow bits, and graham cracker crumbs on top of each ball of dough.
Bake cookies for 8 to 10 minutes, or until crisp around the edges. (If there are any blank areas on the cookies, you can gently press additional toppings into the cookies while they’re still warm from the oven.) Let cookies cool on pans for a few minutes before transferring to a cooling rack.