Lightly grease an 8x8 inch glass or ceramic baking pan with spray and set aside.
Bloom the gelatin. Place the ½ cup of cool water and vanilla bean paste into a small bowl and sprinkle over the gelatin. Set aside to bloom.
Make the sugar syrup. In a large saucepot, mix together the other ½ cup water, corn syrup, sugar, and salt until combined, then set over medium heat.
Stir the sugar syrup mixture with a rubber spatula until it begins to bubble, around 5 minutes, then increase the heat to medium high. Continue to cook without stirring until it becomes clear and a digital thermometer registers 250℉, about another 5 minutes.
Immediately scrape all of the syrup into the bowl of a stand mixer fitted with the whisk attachment. Allow the mixture to cool until 212℉, around 6 minutes, then add in the bloomed gelatin.
Mix on low until the gelatin has melted into the syrup, then increase the speed to medium-high. Whip the meringue for about 10 minutes, until pale white, thick, roughly tripled in volume, and beginning to ball around the whisk.
Reduce the speed to low and add in the melted butter, then increase the speed to medium-high once more and beat for a few more seconds until fully incorporated.
Scrape the marshmallow meringue into the prepared 8-inch pan, spreading it into an equal layer. Cover the pan with foil and refrigerate until firm (about 2 hours) or let stand overnight at room temperature.
To serve. Uncover the marshmallows and sift over a layer of powdered sugar. Using your hands or an offset spatula, invert the marshmallows onto a cutting board and sprinkle over another layer of powdered sugar. Cut the marshmallows into 16 equal pieces with a large chef's knife, being sure to coat each square in a layer of powdered sugar to prevent sticking.
If not using immediately, stack the marshmallows in an airtight container, separating each row with a layer of wax paper. Store the marshmallows at room temperature for up to 3 weeks or in the freezer for 6 months.