In the bowl of a stand mixer, combine 1/2 cup very cold water with the salt and the unflavored gelatin. Stir and allow to sit while you work on the next part.
Combine the remaining water with the white sugar and the corn syrup in a medium saucepan over medium heat. Bring the mixture to a boil stirring frequently. Cover with a lid for exactly 2 minutes. (This gets all the sticking sugar from the sides.)
Stick a thermometer in the pan and without stirring, bring the mixture to 240 degrees F or softball stage. Remove from the stovetop immediately.
Slowly pour the hot syrup over the gelatin mixture while the mixer is on low speed. Once all of the hot syrup has been poured in, turn the mixer to high speed and beat for 12-14 minutes.
Add in the vanilla extract and beat for one more minute.
The bowl will get very full and the mixture will be thick, white, and shiny.
Meanwhile, spray a 9 x 13 cooking sheet with sides with nonstick cooking spray (For thicker marshmallows, you can use a casserole dish). Combine the powdered sugar and cornstarch. Lightly coat the sides and bottom of the pan with the powdered sugar and cornstarch mixture.
Using a lightly greased spatula, spread the mixture evenly on the pan. Lightly coat the top of the marshmallows with the cornstarch and powdered sugar mixture reserving the rest for later.
Allow the marshmallows to cool and set up for at least 4 hours and preferably overnight.
Then using small cookie cutters or sharp kitchen scissors, cut the marshmallows into small pieces and drop the pieces in the remaining cornstarch + powdered sugar mixture. Shake off all of the excess and store in an airtight container in a cool place.