Combine gelatin and cold water in a small saucepan; let stand 5 minutes to soften gelatin.
Place saucepan over low heat and stir until gelatin is dissolved.
Add sugar and stir until sugar is dissolved.
Pour corn syrup in a large bowl (3-4 quart) of electric mixer. Add vanilla and gelatin mixture, and beat about 15 minutes or until mixture becomes thick and of a marshmallow consistency.
Thoroughly cover the bottom of 8 x 8 or 9 x 9-inch pan with equal parts of corn starch and fine granulated sugar.
Pour the marshmallow mixture into the pan and smooth off the top with a knife.
Let stand in a cool place (not refrigerated) until well set, about 1 hour.
To remove from the pan, loosen around the edges with a knife and invert over a board sprinkled lightly with equal parts of corn starch and fine granulated sugar.
Cut into squares with a sharp knife moistened with cold water.
Roll each marshmallow in equal parts of corn starch and fine granulated sugar. Makes about one pound.