Step 1: Grease a 9×13 inch baking pan with a neutral oil or non-stick spray. In a small bowl, whisk together the powdered sugar and cornstarch, then generously dust the prepared pan, tapping out any excess. Set aside.
Step 2: In the bowl of a stand mixer fitted with the whisk attachment, sprinkle the gelatin over 1/2 cup of the cold water. Let it sit undisturbed for 5-10 minutes to bloom and soften.
Step 3: In a medium heavy-bottomed saucepan, combine the granulated sugar, light corn syrup, the remaining 1/2 cup of water, and salt. Stir gently over medium heat until the sugar dissolves completely.
Step 4: Increase the heat to medium-high and bring the syrup to a boil without stirring. Clip a candy thermometer to the side of the pan, ensuring it doesn’t touch the bottom. Cook the syrup until it reaches 240°F (115°C) (soft ball stage).
Step 5: Carefully remove the hot sugar syrup from the heat. With the mixer on low speed, slowly and steadily pour the hot syrup down the side of the bowl into the bloomed gelatin mixture. Be very cautious, as the syrup is extremely hot.
Step 6: Once all the syrup is added, increase the mixer speed to high. Whip the mixture for 10-15 minutes, or until it becomes very thick, glossy, opaque white, and has tripled in volume, forming stiff peaks. Add the vanilla extract during the last minute of whipping.
Step 7: Working quickly, scrape the marshmallow mixture into the prepared pan. Use an oiled spatula or offset knife to spread it evenly. You can also lightly oil your hands to help pat the top smooth.
Step 8: Let the marshmallows set uncovered at room temperature for at least 4-6 hours, or preferably overnight, until firm.
Step 9: Once set, invert the marshmallow slab onto a cutting board heavily dusted with the remaining powdered sugar and cornstarch mixture. Dust the top generously as well. Using an oiled pizza cutter or sharp knife, cut the marshmallows into desired shapes (e.g., 1-inch squares).
Step 10: Toss each cut marshmallow piece in the powdered sugar and cornstarch mixture to coat all sides, preventing sticking. Store in an airtight container at room temperature for up to 2 weeks.