Lightly coat an 8-by-8-inch baking pan with cooking spray.
WHISK TOGETHER the gelatin and cold water in a small bowl and let soften for 5 minutes.
STIR TOGETHER the sugar, 1/4 cup of the corn syrup, water, and salt in a medium saucepan over high heat. Boil, stirring occasionally, until the temperature reaches 240°F. Meanwhile, pour remaining 1/4 cup corn syrup into the bowl of an electric mixer fitted with the whisk attachment. Microwave gelatin on high until completely melted, about 30 seconds. Pour it into the mixer bowl. Set the mixer speed to low and keep it running.
WHEN THE SYRUP reaches 240°F, slowly pour it into the mixer bowl. Increase the speed to medium and beat for 5 minutes. Increase to medium-high and beat for 5 more minutes. Beat on the highest setting for 1 to 2 minutes more and beat in the vanilla; the finished marshmallow will be opaque white, fluffy, and tripled in volume. Pour it into the prepared pan, using an offset spatula to smooth it into the corners. Sift coating evenly and generously over top. Let set for at least 6 hours in a cool, dry place.
Use a knife to loosen the marshmallow from the edges of the pan. Invert the slab onto a coating-dusted work surface and dust it with more coating. Cut into whatever size pieces you wish (a pizza cutter works great for squares). Dip the sticky edges of the marshmallows in more coating, patting off the excess.
Notes
Variation: Super vanilla-ize these mallows by adding a scraped vanilla bean or dab of pure vanilla bean paste along with the vanilla extract.