Brush a 9 by 13-inch glass baking dish with vegetable oil. Cut a piece of parchment or waxed paper large enough to cover the bottom of the dish and to overhang the longer sides. Place the parchment in dish, brush with oil, and set dish aside.
Pour 3/4 cup cold water in the bowl of an electric mixer, and sprinkle the gelatin on top. Let stand for 5 minutes.
Place 3 cups sugar, corn syrup, salt, and 3/4 cup water in a medium saucepan. Set saucepan over high heat, and bring to a boil. Insert a candy thermometer, and cook until mixture reaches soft-ball stage (238 degrees F), about 9 minutes.
In a mixer fitted with the whisk attachment, on low speed, beat the hot syrup into gelatin. Gradually increasing speed to high and beat until mixture is very stiff, about 12 minutes. Beat in the vanilla. Pour mixture into prepared baking dish, and smooth the surface with an offset spatula. Set aside, uncovered, until marshmallow becomes firm, at least 3 hours and up to overnight.
Place 1 cup confectioners' sugar in a fine strainer, and sift onto a clean work surface. Invert large marshmallow onto sugar-coated surface, and peel off parchment paper. Lightly brush a sharp knife with vegetable oil, and cut marshmallow into 12 (2-inch) squares. Sift the remaining 1/2 cup confectioners' sugar into a small bowl, and roll the marshmallows in the sugar to coat. Set aside.
Heat oven to 350 degrees F.
Brush a 9 by 13-inch glass baking dish with melted butter. In a large bowl, combine the graham cracker crumbs, 9 tablespoons melted butter, and remaining 5 tablespoons granulated sugar. Using the back of a spoon, press mixture firmly into the prepared dish. Transfer to oven, and bake until the crust has set, 15 to 20 minutes. Transfer to a wire rack to cool completely.
Bring a medium saucepan of water to a simmer. Place chocolate in a medium heatproof bowl, and set it over simmering water. Melt the chocolate, stirring occasionally. Remove bowl from heat, and stir in butter, 1 piece at a time, until melted and thoroughly combined with chocolate. Pour over cooled graham cracker crust. Using an offset spatula, spread into an even layer. Transfer to refrigerator, and chill until firm, about 30 minutes.
Heat broiler. Cut the chocolate crust into 12 (3-inch) squares. Top each square with a marshmallow, and place the assembled s'mores under the broiler just until the marshmallows turn golden brown, about 20 seconds. Serve immediately.
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