Oil a Pyrex lasagna baking dish with vegetable oil. Line the dish with foil (don’t use the heavy duty stuff) and then lightly coat the foil with oil.
In the bowl of an electric mixer, soften the gelatin with ¾ cup water.
Combine the sugar, corn syrup, ¾ cup water and the salt in a heavy saucepan. Bring to a boil and cook over high heat until the syrup reaches 240 degrees on a candy thermometer.
With the whisk attachment of the mixer at full speed, pour the hot syrup slowly into the gelatin. Continue to beat for 15 minutes. The mixture will be white and fluffy and very stiff. Add the vanilla and beat until completely incorporated. Pour the mixture into the prepared Pyrex pan and smooth the top with a lightly oiled spatula. Allow to rest uncovered for 10-12 hours.
Using a fine sieve, sprinkle powdered sugar onto a cutting surface. Turn the marshmallow mixture onto the powdered sugar, remove and discard the foil and sift more powdered sugar on top of the marshmallow mixture. Cut as desired. Roll the cut marshmallows in more powdered sugar to prevent sticking.