Line a 13×9 inch baking dish with parchment paper (this just makes them easy to remove and cut). If you don’t have parchment, spray the pan with cooking spray, then continue with the instructions. Using a small, fine-mesh sieve, dust the pan generously with confectioners’ sugar.
Put 2/3 water (tap water is fine) in the bowl of a stand mixer with the whisk attachment. Sprinkle the gelatin into the bowl and stir quickly, just enough to make sure all the gelatin is mixed with water. Let soften while you make the sugar syrup.
In a small saucepan, bring 1/2 cup water to a simmer and keep hot, covered (or else it will evaporate, and exact measurements are important).
Meanwhile, in a large saucepan, combine the sugar and 1/2 cup water (not the water simmering, an additional 1/2 cup) and place over medium heat, stirring until the sugar is dissolved. Once the sugar is dissolved, stop stirring and bring the syrup to a boil, washing down the sides of the pan occasionally with a pastry brush dipped in cold water.
Boil the syrup until it begins to caramelize. Continue cooking, swirling the pan gently a few times, until the syrup is a deep golden caramel color (but not burnt. Keep your eye on it!).
Remove the pan from the heat, stand back, and carefully add the 1/2 cup simmering hot water (it will bubble up and steam).
Whisk the caramel until smooth, then whisk in the corn syrup and salt. Return the pan to medium heat and bring the sugar syrup to a boil. Put a candy thermometer into the pan and continue boiling (if the mixture foams up, turn down the heat a little), without stirring, until the thermometer registers 240 degrees.
Remove the pan from the heat.
Turn your mixer on low speed and slowly pour the hot syrup into the softened gelatin in a thin stream down the side of the bowl. Gradually increase the mixer speed as you pour. Increase speed until you’ve reached a high speed. Beat until the marshmallow is very thick and forms a thick ‘ribbon’ when the whisk is lifted, about 5 minutes. Beat in the vanilla (just until incorporated).
With a rubber spatula, scrape the marshmallow into the prepared pan (it’s very sticky!).
Dip your fingertips in water and spread the marshmallow evenly across the pan and smooth the top. Let the marshmallow stand, uncovered, at room temperature until the surface is no longer sticky and you can gently pull the marshmallow away from the sides of the pan (at least 4 hours, preferably overnight).
Lift the parchment paper out of the baking dish and put on a cutting board. Push the sides of the parchment paper down. Dust the top with confectioners’ sugar.
Cut the marshmallows into 1 inch squares (or any zsize you like).
*If your knife is sticking, brush it with vegetable oil and dust with confectioners’ sugar to prevent sticking.
Continue dusting the knife as necessary.
Fill a small bowl with confectioners sugar and dunk each cut marshmallow in it and give it a generous coating. Shake off any excess sugar and place the dusted individual marshmallows in a large dish or bowl.
Marshmallows can be stored, layered between sheets of wax paper or parchment in an airtight container in a dry place at cool room temperature, for 1 month. You can also put them in an airtight container and freeze them. They don’t freeze to be super firm and are a nice little cold treat during the summer!