Oil the bottom of a 9x13x2 pan, dust with powdered sugar.
In your stand mixer's bowl, dust gelatin over cold water and let stand.
In a 3-quart heavy saucepan, cook sugar, corn syrup, hot water, and salt until sugar is dissolved. Turn heat up to medium and boil mixture without stirring until a candy thermometer reaches 240 degrees. About 12 minutes. Remove from heat and carefully pour over gelatin mixture. Stir until gelatin is dissolved.
Beat mixture on high until white, thick, and nearly tripled in volume. About 6 minutes.
In a large bowl, with clean beaters, beat egg whites until they hold stiff peaks. Beat whites and vanilla into sugar mixture until well combined.
Pour mixture in powdered baking pan and dust with a thick layer of powdered sugar. Chill, at least 3 hours, or until marshmallow is firm.
Run a knife around pan and use your fingers to loosen the marshmallow out of pan and onto a large cutting board.
Cut into squares, shapes, anything you'd like, and dust them individually with powdered sugar.
(You can also put them on a stick and dip them in melted chocolate!)
Keep marshmallows in a tightly closed container for up to 4 days.
Great in hot chocolate!