Preheat the oven to 350˚F (180°C). Line a 9"×13" (23x33cm) pan with parchment paper and set aside.
Make the crust by mixing together the graham cracker crumbs, brown sugar, and butter until well combined. Press firmly into the bottom of the prepared pan.
Make the cookie dough: Add the flour, baking soda, salt, and cornstarch to medium mixing bowl and whisk until combined.
Add the butter, brown sugar, and sugar to a large mixing bowl or bowl of a stand mixer fitted with the paddle attachment. Beat until light and fluffy, about 2 minutes. Add the milk and vanilla and beat again until well combined.
Add the dry mixture to the wet and mix until just combined.
Fold in the chocolate chips and marshmallows.
Carefully press the cookie dough evenly on top of the graham cracker crust. Top with the chocolate pieces and gently press them in.
Bake in the preheated oven for 16-18 minutes, until a toothpick comes out clean or with just crumbs.
Allow to cool and slice into 24 bars.