Lightly grease an 8-inch (20cm) or 9-inch (23cm) square baking pan. Then, in a small bowl, combine the powdered sugar and cornstarch and generously sift about one-quarter of the mixture into the pan to cover the bottom and the sides completely.
In a large bowl, using an electric mixer fitted with a whisk attachment, whisk together the gelatin and ½ cup (120 ml) of the water. Let stand until the sugar syrup is done cooking.
In a large saucepan over medium-low heat, combine the remaining ½ cup (120 ml) of water, sugar, salt, and corn syrup, and bring to a low simmer without stirring. Cook the mixture without stirring at any time until it reaches 240°F (116°C), softball stage, about 15 minutes. Use a candy thermometer to check the temperature.
Once the syrup has reached the required temperature, immediately remove it from the heat and pour it into the bowl of bloomed gelatin. Start whisking at low speed and steadily increase the speed to high within the first 30 seconds. Whisk until it is very thick, multiplied several times in size, and still warm to touch; this takes 6 to 10 minutes. Then add the vanilla and whisk just until incorporated, about 30 seconds.
Lightly oil a rubber spatula, and using the oiled spatula, quickly transfer the whipped sugar mixture to the prepared pan. Then, oil your hands and gently even the top by pressing the sugar mixture into the pan. Dust generously with about one-quarter of the powdered sugar mixture. Let it dry for at least 4 hours or overnight.
Run an offset spatula around the sides of the pan. Then invert the pan onto a large tray. Lightly tap the pan to release the marshmallows from the pan. Dust the top with one-quarter of the powdered sugar mixture and let them dry for another 4 hours.
Dust a long, sharp knife with some of the remaining powdered sugar mixture and cut into jumbo or mini marshmallows. If you prefer giant marshmallows, cut them about 2 x 2 inches (5 x 5 cm). After each cut, dust the knife again. Then, toss the marshmallows in the remaining powdered sugar mixture and enjoy. Store them in an airtight container at room temperature for up to 2 weeks.