Pour the 1/2 c cold water and gelatin into the bowl of a mixer.  Allow to bloom for 10 minutes.  

Prepare a 9 x 13 x 2 inch pan as follows. Invert the pan. Cut a piece of aluminum foil long enough to cover the bottom and sides of the pan. Place the foil over the inverted pan and fold down the sides and corners just to shape. Remove the foil and turn the pan right side up. Place the foil in the pan and press it gently into place. With a pastry brush, or crumpled wax paper, or your fingers, coat the foil thoroughly but lightly with vegetable shortening. Set aside. 

Meanwhile, mix the sugar, corn syrup, and 1/4 c water in a saucepan.  Bring to a boil; boil until the sugar's temperature passes 250F.  (This brings the sugar into what is known as the hard-ball stage {when dropping the sugar into some water will form a hard ball that is not easily deformed} and is the traditional temperature of sugar used for making marshmallows).

Mix the gelatin at high speed while drizzling in the boiling sugar syrup.  Once the syrup is mixed in, add 1/4 t salt.  Continue mixing at high speed.  Once the volume of the marshmallow stops increasing, add 1 T vanilla extract.  After the extract is mixed in, stop the mixer.

Pour the marshmallow into the prepared pan and smooth roughly with a spatula.  Let the marshmallow cool and set by leaving it uncovered overnight.  

The next day, invert the pan over a cutting board covered in powdered sugar and peel off the foil.  Use a large greased pizza wheel to section the marshmallows one row at a time, dredging each piece in powdered sugar until the sides aren't sticky anymore.