Liberally spray a 9x13 glass or metal pan with cooking spray. Dust the pan with powdered sugar.
Sprinkle the gelatin over a half cup of the cold water in the bowl of your stand mixer fitted with the wire whisk. Let soften while you cook the syrup.
In a 3 quart heavy bottomed sauce pan, cook the remaining half cup of cold water, sugar, corn syrup, and salt over low heat, stirring with a wooden spoon until the sugar has dissolved. Increase heat to medium and boil until mixture reaches 240 degrees, about 12 minutes.
Remove the pan from the heat and pour the sugar mixture into the stand mixer with the gelatin. Stir to dissolve the gelatin.
Beat on high speed until white, thick, and tripled in volume, about 6 minutes. This will take quite a bit longer if you're using a hand held mixer.
Add the egg whites to a medium bowl and beat with an electric hand mixer until stiff peaks have formed.
Add the egg whites and vanilla to the sugar mixture in the stand mixer and turn to low, mixing until just combined.
Pour the mixture into the prepared baking dish, using a rubber spatula to scrape it out as needed, but being careful not to touch the goo with your hands. You won't get it all out of the bowl and that's okay.
Sift 1/4 cup of powdered sugar over the top of the marshmallows and chill uncovered in the fridge for 3 hours or overnight.
Run a knife along the edges of the pan and turn the marshmallows out onto a cutting board. Cut marshmallows into 1-inch cubes with a sharp knife or pizza cutter.
Sift about 1/2 cup of powdered sugar back into the baking dish and toss the cut marshmallows in it to coat all sides and prevent them from sticking to each other.
Shake off the exceess powdered sugar and store in an airtight container for up to one week.