Preheat the oven to 350 degrees F. Line an 8-inch square baking dish with aluminum foil or parchment, leaving a 2-inch overhang on the ends of the pan for lifting out the finished bars.
Stir together the ground grahams, flour, sugar and salt in a small bowl. Cream the butter, egg and vanilla in a medium bowl with an electric mixer on low speed until creamy and combined; you are not trying to beat a great amount of air into the mixture. Add the graham mixture and continue to beat on low speed until just combined and large crumbles form.
Place about two-thirds of the mixture in the prepared pan and firmly press down. Reserve a few pieces of the chocolate for garnish (about 1/2-ounce), and then scatter the rest of the chocolate pieces over the base. Drop spoonfuls of the marshmallow creme over the chocolate, stretching the creme so it covers more of the base. Drop the remaining cookie batter in small clusters over the chocolate and creme so the creme is mostly covered.
Bake until the dough is golden brown and the cookie in the center of the pan feels firm, about 40 minutes. The marshmallow creme will puff through the crumble and brown, and it will deflate as it cools. Cool in the pan at least 15 minutes.
Using the foil overhang, lift the crumble bars out of the pan. Melt the reserved pieces of chocolate in the microwave in 30-second intervals until smooth, and then drizzle over the cookies. Cut into sixteen 2-by-2-inch squares. Serve warm or at room temperature.
Working with marshmallow creme can be a sticky experience. A light coating of nonstick cooking spray or vegetable oil in your measuring cup and on your spatula or spoon can make it a bit easier to work with.