Preheat the oven to 375°F.
In a large mixing bowl, use an electric hand mixer to cream the salted butter and brown sugar until homogenous.
Whisk in the egg and vanilla on a medium-high speed until the egg is fully incorporated.
Lower the speed of the hand mixer and add the flour, graham crackers, and baking powder. Mix until the dry ingredients are fully mixed into the wet ingredients.
Fold in the chopped chocolate pieces until they are evenly distributed throughout the batter.
Spread the batter into a rectangular baking dish and bake for 30 minutes, or until golden brown.
Remove the pan from the oven, turn the broil to high, and scatter the marshmallow pieces over the top of the dish.
Return the pan to the oven until the marshmallows are golden brown (1-2 minutes).
Allow the bars to cool on the counter before slicing and enjoying.