Prepare the Pan: Line a 9x13 inch baking dish with parchment paper and lightly grease with nonstick spray. Set aside.
Bloom the Gelatin: In the bowl of a stand mixer, combine 1/4 cup of cold water with the gelatin. Let it sit for about 10 minutes to bloom.
Cook the Syrup: In a medium saucepan, combine the remaining 1/4 cup of water, granulated sugar, corn syrup, and salt. Stir over medium heat until the sugar dissolves.Increase the heat to high and cook without stirring until the mixture reaches 240°F (115°C) on a candy thermometer.
Mix the Gelatin and Syrup: With the mixer on low speed, slowly pour the hot syrup into the gelatin mixture. Once all the syrup is added, increase the mixer speed to high. Beat the mixture for about 10-12 minutes, until it becomes thick and glossy.
Add Flavorings: Add the pumpkin puree, vanilla extract, and pumpkin pie spice to the mixture. Beat on high for another 1-2 minutes, until fully combined. Pour the marshmallow mixture into the prepared baking dish, spreading it evenly with a spatula.
Dust with Powdered Sugar and Cornstarch: In a small bowl, mix the powdered sugar and cornstarch together. Dust the top of the marshmallow mixture with some of this mixture.
Set: Let the marshmallows sit at room temperature for at least 4 hours, or overnight, until fully set.
Cut and Serve: Once set, lift the marshmallows out of the pan using the parchment paper. Cut into squares using a sharp knife dusted with the powdered sugar mixture. Toss each marshmallow in the remaining powdered sugar mixture to coat all sides.