In the bowl of your stand mixer, pour ½ cup of cold water and sprinkle the gelatin over it. Let the gelatin bloom for about 10 minutes while you prepare the sugar syrup.
In a medium saucepan, combine the granulated sugar, corn syrup, salt, and the remaining ½ cup of water. Place the saucepan over medium heat and stir until the sugar dissolves. Once the sugar has dissolved, stop stirring and increase the heat to medium-high.
Attach your candy thermometer to the side of the saucepan and cook the syrup until it reaches 240°F (soft-ball stage), which should take about 8-10 minutes.
Once the sugar syrup reaches 240°F, carefully remove it from the heat. Turn the stand mixer to low and slowly pour the hot syrup into the gelatin mixture. Be cautious as the syrup is extremely hot.
After adding the syrup, increase the speed of the mixer to high and beat the mixture for about 10-12 minutes. The marshmallow mixture will turn white, fluffy, and thick. Add the vanilla extract during the last minute of mixing.
While the marshmallow mixture is being whipped, prepare your baking pan by lining it with parchment paper and lightly dusting it with a mixture of powdered sugar and cornstarch. This prevents the marshmallows from sticking to the pan.
Once the marshmallow mixture is ready, pour it into the prepared baking pan and use a spatula to smooth the top. Let the marshmallows sit uncovered for 4-6 hours or overnight to set.
After the marshmallows have set, dust a clean surface with powdered sugar and cornstarch. Turn the marshmallows out onto the surface and cut them into squares using a sharp knife or pizza cutter. Dust each marshmallow with the sugar-cornstarch mixture to prevent sticking.
Store your homemade marshmallows in an airtight container for up to 2 weeks.