Grease a 9x13 inch baking dish with 1 1/2 tbsp oil. Make sure you oil all the way up the sides.
In the bowl of a stand mixer fitted with the whisk attachment, add 1/2 cup cold water and stir in the gelatin and vanilla. Let sit for 15 minutes
In a medium saucepan, add remaining 1/2 cup water, sugar, corn syrup and salt. Bring to a boil over medium high heat, stirring only until the sugar has dissolved. Attach a candy thermometer to the side of the pan, making sure it does not touch the bottom. Boil for 7-8 minutes, or until the mixture reaches 247-250 degrees F.
Take the pan off the heat and remove the thermometer. Turn the mixer to medium-low speed, and slowly pour the hot syrup mixture into the gelatin in a slow, steady stream down the side of the bowl. Gradually increase the speed to medium-high and whip for about 2-3 minutes (to allow the mixture to cool slightly).
Pour in the cake vodka. The marshmallow fluff with become a little watery and less thick. I like to add the vodka once the syrup has cooled slightly so the booze doesn't all burn off.
Continue to whisk for another 15 minutes or so, or until the mixture is thick.
Using a spatula, pour the marshmallow fluff into the prepared 9x13 inch pan (it should come about halfway up the pan). I find that, with the addition of 1/2 cup extra liquid from the vodka, the fluff pours a bit easier and you don't need to fuss with it as much to get it into the pan evenly. Add sprinkles to the top of the marshmallow fluff.
Let the marshmallows sit, uncovered at room temperature for at least 6 hours (preferably overnight).
Once the marshmallows have set and you're ready to cut them, combine icing sugar and cornstarch in a shallow dish and stir to combine. Lightly dust your work surface with this mixture. Using a spatula, release the marshmallows from the pan and out onto your work surface. Once on the counter, flip it over so the sprinkles are on top. Using a sharp knife, cut into desired shape. Once they are cut, you can toss them in the icing sugar mixture, or (because I like the sprinkles to be visible) just dab the cut edges and the bottom into the icing sugar. Tap off excess.
Keep in an airtight container at room temperature for up to 2 weeks.