Lightly spray a 11x9-inch baking pan with cooking spray. Line pan with plastic wrap, leaving a 2-inch overhang on all sides; set aside.
In the bowl of an electric mixer fitted with the whisk attachment, sprinkle gelatin over 1/2 cup cold water; let stand for 10 minutes. In a medium saucepan, combine sugar, corn syrup, and 1/4 cup water. Place saucepan over medium-high heat and bring to a boil; boil rapidly for 1 minute. Remove from heat, and, with the mixer on high, slowly pour the boiling syrup down the side of the mixer bowl into gelatin mixture. Add salt and continue mixing for 12 minutes.
Add vanilla bean paste; mix until well combined. Spray a rubber spatula or your hands with cooking spray. Spread gelatin mixture evenly into pan using prepared spatula or your hands. Spray a sheet of plastic wrap with cooking spray and place, spray side down, on top of marshmallows. Let stand for 2 hours.
Carefully remove marshmallows from pan. Remove all plastic wrap and discard. Cut marshmallows into 2-inch squares using a sprayed sharp knife. Sift confectioners' sugar and cornstarch in a large bowl. Working in batches, add marshmallows to bowl and toss to coat.