In a bowl, combine gelatin with ½ cup cold water. Let it sit for about 5 minutes to soften.
In a saucepan, combine granulated sugar, corn syrup, salt, and the remaining ½ cup of water. Stir over medium heat until sugar dissolves. Then, increase heat and bring the mixture to a boil. Allow it to boil for 1 minute.
Pour the hot sugar mixture over the softened gelatin and beat with an electric mixer on high speed until thick, about 10 to 15 minutes.
Add vanilla extract during the last minute of beating. The mixture should be glossy and hold its shape.
Grease a pan and dust it with powdered sugar. Transfer the marshmallow mixture to the pan and spread it evenly.
Let the marshmallows sit at room temperature for at least 4 hours, or overnight, until set.
Dust a cutting board with powdered sugar, invert the marshmallow slab onto it, and cut into squares using a sharp knife.