Brush a 9-by-13-inch glass baking dish with vegetable oil. Cut a piece of parchment or wax 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 gelatin on top. Let stand 5 minutes.
Place 3 cups granulated 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°), about 9 minutes.
Using the whisk attachment, beat hot syrup into gelatin on low speed. Gradually increasing speed to high, beat until mixture is very stiff, about 12 minutes. Beat in vanilla. Pour mixture into the prepared baking dish, and smooth the surface with an offset spatula. Set dish aside, uncovered, until marshmallow becomes firm, at least 3 hours or overnight.
Place 1 cup confectioners’ sugar in a fine strainer, and sift onto a clean work surface. Invert large marshmallow onto the sugar-coated surface, and peel off the parchment paper. Lightly brush a sharp knife with vegetable oil, and cut marshmallow into 2-inch squares. Sift remaining 1/2 cup confectioners’ sugar into a small bowl, and roll marshmallows in sugar to coat. Set aside.
Preheat oven to 350°. Brush a 9-inch-square baking pan with melted butter. In a large bowl, combine graham-cracker crumbs, 7 tablespoons melted butter, and remaining 1/4 cup granulated sugar. Using your hands, press mixture firmly into the prepared pan. Transfer pan to oven, and bake until the crust has set, 15 to 18 minutes. Remove pan from oven, and transfer to a wire rack to cool.
Bring a medium saucepan of water to a simmer. In a medium heat-proof bowl, combine chocolate with remaining 6 tablespoons butter. Set the bowl over the simmering water, and stir until chocolate and butter have melted. Pour chocolate mixture over cooled graham-cracker crust. Using an offset spatula, spread chocolate mixture into an even layer. Transfer to refrigerator, and chill until firm, about 30 minutes.
Preheat the broiler. Cut chocolate crust into nine 3-inch squares. Top each square with a marshmallow, and place assembled s’mores under the broiler just until marshmallows turn golden brown, about 20 seconds. Serve immediately.