Heat the oven to 350°F. Line an 8-inch-square baking dish with foil, leaving about 1 inch hanging over 2 edges. Lightly coat the bottom and sides with cooking spray. Make room in the fridge.
Put 3 Tbs. of the butter in a medium, heatproof bowl and heat in a microwave or over simmering water until melted. Add the cookie crumbs and stir until the crumbs are moist and well blended. Dump the crumbs into the prepared pan and, using a flat-bottomed cup, firmly press the crumbs into an even layer on the bottom. Bake until fragrant, about 12 minutes. Set on a rack to cool.
Put the chocolate and the remaining 5 tablespoons butter in a medium heatproof bowl and heat in a microwave or over simmering water until melted. Whisk until smooth and blended. Pour into the baked crust (it's OK if the crust is still warm) and spread evenly. Refrigerate until almost firm, about 30 minutes (for faster chilling, slide the pan into the freezer). Arrange the marshmallow halves, cut side down, evenly over the chocolate, pressing lightly. Cover and refrigerate until very firm, about 40 minutes or for up to 2 days.
Just before serving, adjust the oven rack to the top level and heat the broiler on high. Using the excess foil as handles, lift the s'more square from the pan and set on a cookie sheet. Pull the foil away from the sides and slide the cookie sheet under the broiler. Broil until the marshmallows are browned, about 20 seconds. Set on a rack and move the foil and s'more square to a cutting board. Cut into 18 rectangles. Serve immediately or cover and refrigerate for up to 2 days. Serve slightly chilled.
In place of the graham cracker crumbs, switch in 1 cup of gingersnap cookie crumbs.