Sift together the cornstarch and confectioners’ sugar into a medium bowl.
Lay out a clean kitchen towel on the counter. Place a 9-by-13-inch metal baking pan on the towel, then spray generously with nonstick oil spray. Thoroughly dust with 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, pour in 1/2 cup of the water, then sprinkle the gelatin into an even layer over the surface. Let sit for 5 minutes to bloom; if, after 5 minutes, you still see dry gelatin, drizzle on just enough extra water to barely cover. Let that 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 it is running, slowly pour the sugar syrup down the side of the bowl into the gelatin mixture. Do not pour it directly on the whisk. Once you have added all of the syrup, gradually increase the speed to high. Continue to whip until the mixture becomes very thick and the bowl feels just lukewarm to the touch, 13 to 14 minutes in my kitchen. Add the vanilla, then continue to whisk for another 30 seconds to incorporate. Reduce the speed to stir and gradually lift the mixer head to dislodge most of the marshmallow from the whisk. Turn the mixer off.
Pour the mixture into the prepared pan, using a lightly oiled spatula to spread it evenly. The marshmallow will set up quickly, so don’t dawdle. 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, but overnight would be better.
Use a small offset spatula to loosen the marshmallow from the sides of the pan. Turn the marshmallows out onto a cutting board, dust with a little more of the sugar-cornstarch mixture, and, using a pizza cutter or sharp knife rubbed with oil, cut into 24 squares. (You can also cut them into 1/2-inch squares if you’d like mini marshmallows for hot cocoa.) 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 weeks, if not months.