Preheat oven to 350°F. Lightly grease a 9? x 13? pan; line pan with parchment paper or aluminum foil. Arrange the graham crackers over bottom of pan, breaking them so it is completely covered.
Melt butter in a medium-sized bowl using the microwave or in a saucepan over low heat, stir in sugar and cook for two to three minutes, stirring often to dissolve sugar, if using microwave stir in sugar and microwave on half power for 1 minute.
Add mixture to a large bowl and stir in the cocoa, salt, baking powder and vanilla. Stir in eggs until completely mixed in. Add flour and stir until smooth. Stir in marshmallows. Carefully pour into pan and smooth out.
Bake for 30 minutes and cool completely on a wire rack. If desired cover the top with mini marshmallows as soon as you take the pan from the oven. After cooled, refrigerate for 1 – 2 hours. Remove the brownies from the pan, parchment included to a cutting board and cut into squares with a very sharp knife dipped in hot water and wiped clean after each cut.