Make Cookie Dough: In large bowl with electric mixer, cream butter and both sugars on medium speed for 2 to 3 minutes until light and fluffy. Add egg and vanilla, mixing on low until combined. Scrape down bowl.

Add Dry Ingredients: In separate bowl, whisk together flour, baking soda, and salt. Add to wet ingredients and mix on low just until no flour streaks remain. Do not overmix. Fold in chocolate chips and 1 cup mini marshmallows until evenly distributed.

Prepare Pan: Preheat oven to 350°F (175°C). Line 8x8-inch pan with parchment paper, leaving overhang on two sides. Break graham crackers to fit bottom of pan, covering as much surface as possible.

Assemble: Drop spoonfuls of cookie dough over graham crackers. Gently press and spread into even layer covering all crackers. Wet hands slightly if dough is too sticky.

Bake: Bake for 25 to 30 minutes until edges are golden and pulling away from sides. Center should look set but may seem slightly soft. Do not overbake.

Toast Marshmallows: Remove from oven and immediately scatter remaining 1 cup mini marshmallows on top. Turn oven to broil. Place pan under broiler 6 inches from heat. Broil for 1 to 2 minutes, watching constantly, until marshmallows are golden with brown spots.

Add Chocolate: Remove from oven immediately and press chocolate bar pieces into hot surface. Chocolate will begin to melt from residual heat. Let cool completely in pan, at least 2 hours.

Cut and Serve: Use parchment overhang to lift bars from pan. Place on cutting board and cut into 16 squares with sharp knife, wiping knife clean between cuts. Serve at room temperature or slightly warm.