Line a square container with parchment paper and grease the paper with oil.
Pour 1/3 cup of cold water into the bowl of an electric mixer and sprinkle the powdered gelatin on top. Let sit for 5 minutes.
Place the sugar and ¼ cup cold water in a small pot and set to medium-high heat. Stir until the sugar has melted.
Attach a candy thermometer to the pot and boil the sugar until it reaches 238F. Brush the sides of the pot with a wet pastry brush if sugar crystals stick to the sides. Add the peppermint extract and mix well.
Add the hot sugar to the gelatin and stir the mixture by hand whisking for a few minutes to slightly cool. Then beat with an electric mixer on medium-high speed for 8-10 minutes, until soft peaks form.
Pour the marshmallow into the container and dot with the hot pink food colouring. Use a toothpick to swirl the food colouring around to create a pretty pattern. Allow the marshmallow to set for 3-4 hours (or up to overnight) until firm.
Dust the marshmallows with corn starch. Dip a candy cane-shaped cookie cutter in corn starch and cut out candy canes from the marshmallow. Flip the candy canes over and dust the underside with corn starch. Place the marshmallows in a sieve and bounce a few times to remove any excess corn starch.