In a small bowl, combine the gelatin with 1/2 cup of cold water. Allow it to sit and bloom for about 10 minutes.
In a large saucepan over medium heat, combine the granulated sugar, light corn syrup, 1/2 cup of water, and salt. Stir until the sugar dissolves, then stop stirring and allow the mixture to boil.
Use a candy thermometer to monitor the temperature; you want it to reach 240°F (soft ball stage).
Once your sugar mixture reaches the desired temperature, remove it from the heat and carefully pour it into the bowl of your stand mixer (with the bloomed gelatin) while the mixer is running on low speed.
Gradually increase the speed to high and whip for about 10 minutes, or until the mixture becomes thick, glossy, and tripled in volume.
Add the vanilla bean paste and coconut extract to the marshmallow mixture. Mix for an additional minute to incorporate the flavors fully.
Lightly grease your 9x13 inch baking pan with vegetable oil. In a separate bowl, combine the cornstarch and powdered sugar.
Dust the bottom of the greased pan with a generous amount of this mixture to prevent sticking.
Pour the marshmallow mixture into the prepared pan, using a spatula to spread it evenly. Dust the top with more of the cornstarch and powdered sugar mixture.
Allow the marshmallows to set at room temperature for at least 4 hours, or overnight for best results.
Once set, use a sharp knife dusted with the cornstarch mixture to cut the marshmallows into squares. Toss them in the remaining cornstarch and powdered sugar to coat all sides.