Spray a 9×13-inch glass or ceramic baking pan with cooking spray (avoid metal, as it may affect the flavor). In a small bowl, mix the powdered sugar and cornstarch, then generously dust the pan with the mixture, reserving some for dusting the marshmallows at the end.
In the bowl of the stand mixer fitted with a whisk attachment, or using a hand mixer, add the gelatin and ⅔ cup cold water. Mix together for 30 seconds, then let sit to bloom for 20 minutes.
In a medium heavy-bottomed saucepan over medium-high heat, whisk together the sugar, salt and remaining 1 cup of water. Bring to a boil and boil for about 15 minutes, until the mixture reaches 240°F.
With the mixer running on low, slowly pour the hot sugar mixture into the gelatin. Increase the speed to medium-high and beat for 10 minutes, until it becomes thick and fluffy and forms soft peaks.
Beat in the egg whites and mix for another 5 minutes. Mix in the vanilla extract and the vanilla bean seeds.
Pour the marshmallow into the prepared pan, then smooth it into an even layer. Let it sit uncovered at room temperature for at least 8 hours, or up to 48 hours.
Once the marshmallow is firm, prepare a parchment-lined surface dusted with the remaining cornstarch/sugar mixture.
Use a sharp knife to loosen the edges, then gently peel the marshmallow from the pan and turn it out onto the prepared surface.
Lightly coat a knife with the cornstarch/sugar mixture (or run it under hot water and dry) for clean cuts. Cut the marshmallow into 1.5-inch squares, dusting the edges of each square in the remaining cornstarch/sugar mixture to prevent sticking.