Oil bottom and sides of a 13x9x2-inch rectangular metal baking pan and dust bottom and sides with some confectioners' sugar.
In bowl of a standing electric mixer or in a large bowl sprinkle gelatin over cold water and let stand to soften.
In a 3-quart heavy saucepan cook granulated sugar, corn syrup, hot water, and salt over low heat, stirring with a wooden spoon, until sugar is dissolved. Increase heat to moderate and boil mixture, without stirring, until a candy or digital thermometer registers 240°F., about 12 minutes. Remove pan from heat and pour sugar mixture over gelatin mixture, stirring until gelatin is dissolved.
With standing or a hand-held electric mixer beat mixture on high speed until white, thick, and nearly tripled in volume, about 6 minutes if using standing mixer or about 10 minutes if using hand-held mixer. In a large bowl with cleaned beaters beat whites (or reconstituted powdered whites) until they just hold stiff peaks. Beat whites and vanilla into sugar mixture until just combined. Pour mixture into baking pan and sift 1/4 cup confectioners' sugar evenly over top. Chill marshmallow, uncovered, until firm, at least 3 hours, and up to 1 day.
Run a thin knife around edges of pan and invert pan onto a large cutting board. Lifting up 1 corner of inverted pan, with fingers loosen marshmallow and let drop onto cutting board. With a large knife trim edges of marshmallow and cut marshmallow into roughly 1-inch cubes. Sift remaining confectioners' sugar into a large bowl and add marshmallows in batches, tossing to evenly coat. Marshmallows keep in an airtight container at cool room temperature 1 week.