Combine the gelatin and 1/2 cup (113g) cool water in the bowl of an electric mixer fitted with the whisk attachment. Mix briefly to combine; set aside., Combine the sugar, corn syrup, salt, and 1/2 cup (113g) cool water in a small, deep saucepan. Cook the mixture over medium heat, stirring, until the sugar dissolves., Raise the heat to high and cook, without stirring, until the syrup reaches 240°F on a candy thermometer. Remove from the heat., With the mixer set on low speed, slowly pour the sugar syrup into the softened gelatin. Increase the speed to high, and whip until the mixture is very thick and fluffy, and has cooled to lukewarm, 3 to 10 minutes (depending on the mixer and attachment you use; a stand mixer using the whisk attachment will work more quickly than a hand mixer equipped with beaters). The mixture should be cool enough that you can spread it into the pan without burning your fingers, about 95°F. Add vanilla towards the end of the mixing time., Spread the marshmallow mixture into a greased 9" x 13" pan (glass or ceramic is best). Use your wet hands to smooth and flatten the marshmallows., Sprinkle confectioners' sugar over the top, and let sit for several hours (or overnight) before cutting. Use a greased knife or cookie cutters to make squares or other shapes. Dipping the knife or cutters in cold water before cutting helps reduce any stickiness., For gift-giving, wrap marshmallows individually in twists of waxed paper, and store at cool room temperature. For storage, place in a closed container, the layers separated by waxed paper or parchment paper.