Pink Peppermint Swirl Marshmallows

Brush bottom and sides of metal pan with some vegetable oil.
Put 1/2 cup water in bowl of stand mixer and sprinkle gelatin over it. Stir it briefly to make sure all the gelatin is in contact with water and let it soften while making the syrup.
Heat sugar, corn syrup, salt, and remaining 1/2 cup water in a small heavy saucepan over low heat, stirring until sugar has dissolved, then bring to a boil over medium heat, without stirring.
Put thermometer into syrup and continue boiling, without stirring, until it registers 240°F (soft-ball stage). Remove from heat and let stand until bubbles dissipate.
With mixer at low speed, pour hot syrup into gelatin in a thin stream down side of bowl. Increase speed to high and beat until very thick and the mixture forms a thick ribbon when beater is lifted, about 5 minutes. Beat in peppermint.
Quickly scoop about two-thirds of still warm marshmallow into another bowl. Add the red food coloring to the remaining one-third marshmallow and beat it to combine.
Working quickly, fill the prepared pan with alternating dollops of the white and pink marshmallow (it will be very sticky), then swirl a knife through the mixture to marble it. Smooth the surface with dampened fingertips. Let stand, uncovered, at room temperature until surface is no longer sticky and you can gently pull marshmallow away from sides of pan with your fingertips, 2 to 3 hours.
Using a sieve, dust a cutting board with confectioners' sugar. Use a spatula to pull sides of marshmallow from edge of pan, then invert onto cutting board. Dust top with confectioners' sugar. Cut lengthwise into 8 strips, then crosswise into eighths, to form a total of 64 squares.
Coat marshmallows, one at a time, in confectioners' sugar, shaking off excess.