Preheat the oven to 350 degrees Fahrenheit. Lightly spray a 10-inch cast iron skillet with cooking spray and set aside.
To a medium bowl add flour, crushed graham crackers, salt, and cocoa powder. Whisk to combine and set aside.
Place a large stainless steel bowl over a small saucepan half-full of simmering water. Add the chocolate and butter to the bowl. Stirring occasionally, allow the butter and chocolate to melt completely. Turn off the heat and remove the bowl from the pot of simmering water. Add the granulated and brown sugar and whisk to completely combine. Set aside and allow the mixture to come to room temperature.
Add 3 eggs to the chocolate/sugar mixture and whisk until the eggs are combined. Add the remaining eggs (2) and whisk until combined. Stir in the vanilla bean paste until combined the mixture takes on a pudding texture. Be sure not to over-whisk.
Sprinkle the flour/graham cracker mixture over the chocolate mixture and with a rubber spatula, fold until somewhat combined, but can still see bits of flour. Add about ¾ cup of chocolate chips and fold until mostly combined.
Pour brownie batter in the skillet. Sprinkle the remaining ¼ cup of chocolate chips over the brownie batter.
Place skillet in the oven and bake for 35-40 minutes, rotating the pan midway through baking. What you’re looking for is the edges to be set, yet the middle to jiggle a bit when the pan is moved.
Remove skillet from the oven. Allow the brownies to cool at room temperature for at least 10-15 minutes.
Raise the oven temperature to 450° Fahrenheit.
Arrange the marshmallows over the baked brownies. Place in the oven for about 4-5 minutes until the marshmallows have melted, expanded, and browned. Remove from the oven and allow to cool.
Sprinkle with crushed graham crackers and serve warm, with some ice cream on the side, if desired.
Leftovers can be covered at room temperature with plastic wrap for up to 3 days.