Line a 9x9-inch square pan with plastic wrap, then spray the plastic wrap with cooking spray. Spray a rubber spatula with cooking spray as well to use later. Set aside.
Stir all of the powdered gelatin into ½ cup of the water in a small bowl, then let it sit for 5 minutes to bloom. Once the gelatin is a firm lump, dump it in the bowl of a stand mixer fitted with a whisk attachment.
Combine the remaining ¼ cup of water, sugar, corn syrup, and salt in a heavy duty medium saucepan over medium heat. Bring to a boil, stirring occasionally, until the mixture reaches 235 to 240°F on a candy thermometer stuck on the side of the pan.
Slowly pour the hot sugar syrup in a thin stream over the gelatin in the mixer while it is running on medium speed over the course of 1-2 minutes. Once all of the liquid has been added, increase the speed to high and beat for 10 minutes, until fluffy and the marshmallow mixture has more than doubled in volume. Add the vanilla extract during the last minute of mixing to flavor the marshmallows.
Pour the marshmallow mixture into the prepared baking dish using the rubber spatula sprayed with cooking spray to scrape it all out of the ball and to smooth it into the corners of the pan as needed.
Whisk the powdered sugar and cornstarch together in a medium bowl, then sift about 2-3 tablespoons of this mixture over the marshmallow in the pan to cover the top. Reserve the rest for later.
Let the pan of marshmallow rest for at least 4 hours or overnight.
Turn out the pan of marshmallow onto a clean surface. Peel off the plastic wrap, then dust generously with more of the powdered sugar mixture. Spray a pizza cutter or pair of kitchen scissors with cooking spray and cut the slab of marshmallow into six columns, then across in six rows to create 36 large marshmallows. Dust generously with the remaining powdered sugar mixture while cutting to prevent the fresh marshmallows from sticking to each other.
Shake off excess powder before storing in an airtight container. I find it easiest to throw a handful of the marshmallows into a fine mesh sieve and shake them around in it to get the excess powder off. Enjoy!