Grease a sheet tray and set aside. Bloom the gelatin in cold water for 5 to 10 minutes. Meanwhile, combine the corn syrup and half of the sugar in a small pot and heat to 250ºF. Remove from the heat. Squeeze the excess water out of the gelatin sheets, then add the gelatin sheets to the syrup while still hot. Add the vanilla bean paste. In a standing mixer, whip the remaining half of the sugar and the egg whites together to a firm peak. With the mixer on speed 2, slowly pour the hot syrup into the whipped egg whites, whisking until the mixture cools to 115ºF. Spread the mixture evenly on the prepared sheet tray, cover, and cool completely. Cut into desired shapes.