Preheat the oven to 350 degrees Fahrenheit. Spray a 9"x13" pan with nonstick baking spray.
In a large bowl, stir together graham cracker crumbs, melted butter and sugar until all the crumbs are coated and moist. Press into the pan. Use the bottom of a measuring cup to pack the crumbs down.
Bake crust for 9-10 minutes.
While the crust is baking, make the brownies. In a large microwave-safe bowl, melt butter and chocolate chips together in 30 second increments, stirring between. Stir mixture until smooth. Quickly whisk in (by hand) brown sugar, white sugar, vanilla, eggs, and milk, just until incorporated (don’t over-mix or brownies will be tough and lose their nice texture). Add flour, baking cocoa, baking powder, salt and corn starch to the bowl and stir by hand just until incorporated.
Quickly and carefully pour and spread brownie mixture over baked crust (batter will start to melt and bake on the hot crust). Bake for approximately 15-16 minutes, or just until brownies are set.
While brownies are baking, cut the marshmallows in half. Break apart chocolate bars and keep in the fridge.
Immediately after brownies are done baking, remove them and set the oven to BROIL. Place the marshmallows on the top of the baked brownies, cut side down, close together so they're touching each other. Place the brownies under the broiler and watch them THE ENTIRE time, just until the marshmallows are golden brown (this took less than a minute for me). Immediately remove them and push cold chocolate bar pieces into the marshmallows. Immediately place the brownies in the fridge so the chocolate pieces won't melt too much. Let brownies cool completely in the fridge, so the chocolate pieces can harden, then remove them and store at room temperature. Slice and serve.