Grease a 9x13 baking dish and set aside.In the bowl of a stand mixer fitted with a whisk attachment, combine the gelatin and 1/2 cold water. Set aside to "bloom". In a medium saucepan, combine the white sugar, corn syrup, salt, and 1/2 cup water.
Attach a candy thermometer to the side of the pan (make sure the thermometer is submerged in the liquid but not touching the bottom), and heat over medium-high heat until the mixture reaches 240° - about 10 minutes. *You can swirl the pan occasionally, but don't stir it much - it can cause the sugar to crystalize. When the sugar mixture reaches 240°, remove from the heat.
With the mixer on low speed, slowly pour a thread of the sugar mixture down the side of the mixing bowl into the gelatin mixture. (If you add the hot mixture to the gelatin too quickly, it will "cook" the gelatin and the marshmallows won't set up well.)
Once all of the sugar mixture has been added to the gelatin, beat on high speed until the mixture is very thick and forms stiff peaks - about 15 minutes. Then add the vanilla and mix thoroughly.
Pour the marshmallow mixture into the prepared pan and smooth the top.
In a small bowl, combine the powdered sugar and cornstarch then, using a sifter or sieve, generously sprinkle over the top of the marshmallows. (Save the leftover sugar/cornstarch mixture for later.)
Allow the marshmallows to sit, uncovered and at room temperature, for 4-6 hours or overnight.
Once the marshmallows are completely set, dust a knife with the leftover powdered sugar/cornstarch mixture and cut the marshmallows into bite-sized squares.
Remove the cut squares and roll them in the sugar/cornstarch mixture so they are thoroughly coated - this will keep them from sticking together.