Heat oven to 350°F. Grease 8-inch square baking pan.
Beat butter and sugar until well blended in large bowl. Add egg and vanilla; beat well. Stir together flour, graham cracker crumbs, baking powder and salt; add to butter mixture, beating until blended. Press half of dough in prepared pan. Bake 15 minutes.
Break chocolate bars into pieces; sprinkle over baked layer. Top with marshmallows; scatter bits of remaining dough over marshmallows, forming top layer. Bake 10 to 15 minutes or just until lightly browned. Cool completely in pan on wire rack. Cut into bars.
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