Pour the 1/2 cup cold water into a stand mixer fitted with a whisk attachment. Sprinkle the gelatin evenly over the water and set aside to bloom (soften and absorb water).
In a small, heavy-bottomed pot, combine the sugar, corn syrup, 1/2 cup water, and salt. Stir together to moisten the sugar. Then, without stirring, bring to a boil over high heat. Insert a candy thermometer into the mixture, making sure it doesn’t touch the bottom of the pot (this will give an incorrect reading). Cook the sugar syrup to 240°F (soft ball stage).
As soon as the mixture reaches 240°F, remove it from the heat. Turn the mixer on high speed and slowly stream the hot sugar mixture into the softened gelatin. Slowly drizzle the syrup on the sides so it doesn’t splash around and make a mess. Once all the syrup has been drizzled in, whip on high until it is cool to the touch, about 10–15 minutes. The mixture will turn from milky white to very fluffy and full.
In the last minute or so of whipping, add in vanilla bean paste and coconut extract.
While the marshmallow mixture is whipping, sift together the cornstarch and powdered sugar in a small bowl.
Line the bottom of a 8x8-inch baking pan with parchment paper, then rub the parchment paper with a little vegetable oil. Sprinkle a few tablespoons of the cornstarch-powdered sugar mixture evenly across the parchment.
When the marshmallow mixture has thickened and cooled, scrape it into the prepared baking pan and smooth it out with a spatula dipped in water. Be prepared—the mixture is extremely sticky! Dust the top with a few tablespoons of the cornstarch-powdered sugar mixture (don’t use it all). Make sure all parts of the marshmallow cool completely, then tightly wrap the pan with plastic wrap. Let it sit overnight at room temperature.
The next day, run a paring knife along the sides of the baking pan and invert the marshmallow slab onto a cutting board. Peel off the parchment and use a sharp knife (dipped in hot water and dried off) to cut the marshmallow into cubes about 1-1/2 inches square (5 rows by 5). Dip the knife in hot water and dry it off before each slice for easiest slicing. Toss each cube in the remaining cornstarch-powdered sugar mixture to coat.
Notes
Storage: Marshmallows can be stored in an airtight container at room temperature for up to 1 month.