Roughly chop the Graham crackers and Hershey's bar, then tear the mini marshmallows in half. Smaller marshmallow pieces stay tucked into the dough more easily and are less likely to flood the pan.
Whisk together the flour, salt, baking powder, baking soda, and cornstarch in a bowl, then set the mixture aside. Make sure everything looks evenly combined with no streaks so the cookies bake with a uniform lift and texture.
Beat the butter with the granulated sugar and light brown sugar for about 2 minutes, then mix in the egg and vanilla and scrape the bowl before mixing once more. The mixture should look creamy and lighter in texture, which means the butter and sugars are properly blended for a chewy cookie structure.
Add the dry mixture gradually to the butter mixture and mix on low speed only until the flour disappears. Stop as soon as the dough comes together so the cookies stay tender instead of turning tough.
Set aside a handful of the torn marshmallows, then mix the remaining marshmallows, chocolate chips, and Graham crackers into the dough on low speed until just combined. The dough should look thick and studded throughout, with graham cracker pieces dispersed in every scoop.
Refrigerate the dough for 1 hour or more. This chill firms the butter, reduces spreading, and gives the marshmallows a better chance of staying inside the cookies.
Heat the oven to 350°F, scoop roughly 2 tbsp portions of dough, roll them into balls, and place them about 2 inches apart on a parchment-lined baking sheet. If the dough starts feeling greasy or loose while rolling, pause and chill it again before baking.
Bake for 8 minutes, top each cookie with the reserved marshmallow pieces and chopped Hershey's bar, then return the pan to the oven for 2 to 3 minutes. The edges should be lightly golden while the centers still look soft, and hot marshmallow sugar can burn badly so do not touch the tops right away.
Leave the cookies on the pan to cool completely. They will finish setting as they cool, and the marshmallow will become chewy instead of flowing everywhere.