Sift together the cornstarch and confectioners’ sugar into a medium bowl.
Lightly spray a 9-by-13-inch metal baking pan with nonstick oil spray. Re-sift about one-third of the cornstarch-sugar mixture over the bottom and sides of the pan, then shake and tap the pan to make sure the mixture coats then pan evenly. Return any remaining mixture to the bowl for later use. Stash the baking pan within arm’s reach.
In the bowl of a stand mixer fitted with the whisk attachment, add the gelatin to 1/2 cup of the cold water. Let sit for 5 minutes to bloom; if, after 5 minutes, you still see dry gelatin, drizzle about 1/2 teaspoon more water over the dry spots and let sit for another minute or two to hydrate.
Meanwhile, combine the remaining 1/2 cup water, the granulated sugar, corn syrup, and the salt in a 2-quart saucepan. Place over medium-high heat, cover, and allow to cook until the mixture begins to simmer around the edges of the pot, about 3 minutes. Uncover and continue to cook, without stirring, until the mixture reaches 240°F on a digital instant-read thermometer, approximately 8 more minutes. If you notice sugar crystals forming on the sides of the pot, use a wet pastry brush to wipe down and dissolve the crystals. When the mixture reaches the target temp, immediately remove from the heat.
Turn the mixer to low speed and, while running, slowly pour the sugar syrup down the side of the bowl into the gelatin mixture. Once you have added all of the syrup, increase the speed to high. Continue to whip until the mixture becomes very thick and is lukewarm, about 15 minutes. Add the vanilla during the last minute of whipping.
Pour the mixture into the prepared pan, using a lightly oiled spatula to spread it evenly. Dust the top with enough of the remaining sugar and cornstarch mixture to lightly cover. Reserve the rest for later. Allow the marshmallows to sit uncovered for at least 3 hours and up to overnight.
Turn the marshmallows out onto a cutting board and, using a pizza cutter or sharp knife rubbed with oil, cut into 1- to 2-inch squares for full-sized marshmallows or 1/2-inch squares for minis. Once cut, lightly dust all sides of each marshmallow with the additional cornstarch-sugar mixture. Consume right away or store in an airtight container for up to 3 weeks.