In a small bowl, combine the gelatin with 1/2 cup of cold water. Allow it to sit for about 5 minutes to bloom.

In a saucepan, mix the granulated sugar, corn syrup, salt, and 1/4 cup of water. Cook over medium heat, stirring until the sugar dissolves. Bring the mixture to a boil and let it cook without stirring until it reaches 240°F on a candy thermometer.

Once the sugar mixture reaches the correct temperature, remove it from heat. Add the bloomed gelatin and stir until dissolved.

In a separate bowl, beat the pumpkin puree, pumpkin pie spice, and vanilla extract until combined.

Slowly pour the hot sugar mixture into the pumpkin mixture while continuously beating on high speed. Continue to beat for about 10-15 minutes, or until the mixture becomes thick and fluffy.

Spread the marshmallow mixture into a greased 9x13 inch pan, smoothing the top with a spatula. Dust with powdered sugar.

Allow the marshmallows to set for at least 4 hours at room temperature before cutting them into squares.