Step 1Set aside a lightly buttered (bottom and sides) 13x9-inch baking pan. Place the gelatin in a small dish; stir in the cold water and set aside.
Step 2Place 1/4 cup of the corn syrup in the bowl of an electric mixer. Combine the hot water, remaining 1/4 cup corn syrup and the granulated sugar in a small saucepan. Stir until the sugar dissolves, then boil uncovered, without stirring, until the mixture registers 230 degrees on a candy thermometer, about 5 minutes.
Step 3Add to the mixer bowl. Whip on medium high, slowly adding the gelatin mixture by spoonfuls. Continue whipping until the outside of the bowl feels cool to the touch and the mixture is thick, about 10 minutes. Add the vanilla; mix until combined.
Step 4Spread the mixture evenly in the pan (it will be about 1/2 inch thick). Let it rest at room temperature, uncovered, for 24 hours. Use a paring knife dipped into hot water to cut the marshmallows into 2-inch squares.
Step 5Place the powdered sugar in a shallow bowl. Toss the marshmallows in the sugar to keep them from sticking. These can be stored up to 5 days at room temperature in an airtight tin, layered between pieces of wax paper.