Preheat oven to 350 degrees Line a 9 x 13 inch pan with parchment paper, leaving an overhang on two opposite sides. Spray lightly with nonstick spray.
In a medium bowl, combine flour, graham cracker crumbs, baking powder and salt; set aside.
In a medium saucepan, melt butter over low heat. Stir in brown sugar just until moistened. Remove from heat and let cool slightly. Whisk in egg and vanilla. Stir in flour mixture just until combined.
Pour batter into prepared pan, smoothing out and spreading evenly. Spread half of chocolate pieces over top.
Bake until toothpick inserted into center comes out clean, about 20-25 minutes. Remove from oven and spread remaining chocolate pieces and marshmallows over top and bake until marshmallows are a pale golden color, about 7-8 minutes. Cool completely in pan on wire rack. Refrigerate for at least 1 hour before cutting. Lift out of pan by parchment paper handles and cut into 24 bars. Serve.