Place the gelatin into the bowl of a stand mixer along with 1/2 cup cold water. Have the whisk attachment standing by.
In a small saucepan, combine the remaining 1/2 cup cold water, sugar, corn syrup and salt. Place over medium high heat, cover and allow to cook for 3 to 4 minutes. Uncover, clip a candy thermometer onto the side of the pan and continue to cook until the mixture reaches 240 degrees, approximately 7 to 8 minutes. Once the mixture reaches this temperature, immediately remove from the heat.
Turn the mixer on 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 the syrup, increase the speed to high. Continue to whip until the mixture becomes very thick and is luke-warm, approximately 12 to 15 minutes. Add the vanilla during the last minute of whipping. While the mixture is whipping, prepare the pans as follows.
For regular marshmallows: Combine the powdered sugar and cornstarch in a small bowl. Lightly spray a 9x13-inch metal baking pan with a nonstick cooking spray. Add the sugar/cornstarch mixture and move around to completely coat the bottom and sides of the pan. Return the remaining sugar/cornstarch mixture to the bowl for later use.
When ready, pour the marshmallow mixture into the prepared pan, using a lightly oiled spatula for spreading evenly into the pan. Dust the top with enough of the sugar/cornstarch mixture to lightly cover. Reserve the rest for later. Allow the marshmallows to sit uncovered for at least 4 hours and up to overnight.
Turn the marshmallows out onto a cutting board and cut into 1-inch squares using a pizza wheel dusted with the sugar/cornstarch mixture. Once cut, lightly dust all sides of each marshmallow with the remaining sugar/cornstarch mixture. Store in an airtight container for up to 3 weeks.
For miniature marshmallows: Combine the powdered sugar and cornstarch in a small bowl. Line 4 half sheet pans with parchment paper, spray the parchment paper with nonstick cooking spray and dust with the sugar/cornstarch mixture.
Scoop the marshmallow mixture into a piping bag fitted with a 1/2-inch round piping tip. Pipe the mixture onto the prepared sheet pans lengthwise, leaving about 1-inch between each strip. Sprinkle the tops with enough of the sugar/cornstarch mixture to lightly cover. Let the strips set for 4 hours or up to overnight.
Cut into 1/2-inch pieces using a pizza wheel or scissors dusted in the sugar/cornstarch mixture. Once cut, lightly dust all the sides of each marshmallow with the remaining sugar/cornstarch mixture and store in an airtight container for up to a week.
Variation: Mocha-Mallows: Substitute Cold Espresso for Cold Water, and substitute Cocoa Powder for Powdered Sugar.