Prepare a 13×9” (33x23cm) pan by lightly but thoroughly greasing the sides and bottom with vegetable shortening. Grease a rubber spatula as well and set it aside nearby.
Prepare dusting powder by whisking together powdered sugar and cornstarch until well-combined. Set aside.
Pour ice water into the bowl of a stand mixer fitted with a whisk attachment and sprinkle the gelatin overtop. Briefly stir to combine.
In a medium-sized, heavy-bottomed pot, combine your sugar, corn syrup, remaining ½ cup (118ml) water and salt and stir to combine.
Turn your stovetop heat just a notch above medium and cook, stirring frequently, until sugar is dissolved. If you notice sugar crystals on the side of the pot, use a damp pastry brush to gently wash them down the sides of the pot back into the mixture.
Continue to stir until mixture comes to a boil, then attach a candy thermometer to the pot (make sure the end of the thermometer is suspended in the middle of the mixture and that it is not touching the bottom of the pot!) and continue to cook without stirring until mixture reaches 242F (115C).
Remove syrup from heat and turn stand mixer speed to low. With mixer on low speed, gradually drizzle the hot syrup into the gelatin mixture in a steady stream. Once all syrup has been added, gradually increase mixer speed to high.
Beat on high-speed for at least 10 minutes/until mixture is fluffy, thick, glossy, and greatly increased in volume.
Add peppermint extract and vanilla extract and stir until completely combined.
Use your greased spatula to pour/spread marshmallow mixture into prepared pan. Immediately dot surface with several drops of red food coloring and use a knife to swirl the color through the marshmallow as desired (try to not scrape the bottom of the pan with your knife–this may scrape away the shortening/powder mixture and your marshmallows may stick to the pan).
Sift 2-3 Tablespoons of the dusting mixture (save remaining mixture, you’ll need it) over the surface of the marshmallows.
Let marshmallows sit at room temperature until firm, at least several hours or overnight.
Once firm, dust a cutting board generously with about a tablespoon of the dusting mixture and pour the remaining mixture in a bowl.
Turn out the marshmallows onto a cutting board and use a greased knife or greased kitchen shears to cut into squares. Toss marshmallows one at a time in bowl with remaining dusting mixture then shake off excess and enjoy.