Preheat the oven to 350°F (175°C).
Prepare a 9x13 inch baking pan by greasing it or lining it with parchment paper.
In a medium saucepan, melt together the butter, granulated sugar, and brown sugar over medium heat, stirring until smooth.
Remove from heat and allow to cool slightly, then whisk in the eggs and vanilla extract until fully combined.
Sift together the flour, cocoa powder, baking powder, and salt in a separate bowl.
Gradually fold the dry ingredients into the wet mixture until just combined, then stir in the chocolate chips.
Pour the brownie batter into the prepared pan, spreading it evenly.
Sprinkle the graham cracker crumbs over the brownie batter, followed by the mini marshmallows.
Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Let the brownies cool in the pan for about 15 minutes, then drizzle with chocolate sauce if desired, before slicing.