1) Combine the gelatin and 1/2 cup of the cool water in the bowl of an electric mixer fitted with a whisk attachment. Set the bowl aside.
2) Combine the sugar, corn syrup, salt, and the remaining 1/2 cup cool water in a small, deep saucepan.
3) Cook the mixture over medium heat, stirring, until the sugar dissolves.
4) Raise the heat to high and cook, without stirring, until the syrup reaches 238°F to 240°F on a candy or digital thermometer. Remove from the heat.
5) With the mixer on low speed, slowly pour the sugar syrup into the softened gelatin. Increase the speed to high, and whip until the mixture is very thick and fluffy, and has cooled to lukewarm, 3 to 10 minutes (depending on the mixer and attachment you use; a stand mixer using the whisk attachment will work more quickly than a hand mixer equipped with beaters). The mixture should be cool enough that you can spread it into the pan without burning your fingers, about 95°F. Don't let the marshmallow get so thick that it forms a stiff ball inside the wire whisk; it shouldn't be as stiff as meringue icing.
6) Add the peppermint oil towards the end of the mixing time.
7) When the marshmallow is fully whipped, add the peppermint crunch and red gel paste, and mix just until you can see swirls of red and white.
8) Spread the marshmallow into a greased 9" x 13" pan (glass or ceramic is best) — a greased dough scraper is helpful here.
9) Use your wet fingers to smooth and flatten the marshmallow into the pan. Sprinkle glazing or confectioners' sugar over the top, and let sit for several hours (or overnight) before cutting.
10) Use a greased knife or cookie cutters to make squares or other shapes. Wrap marshmallows airtight, and store for several days at room temperature.
Yield: about 2 dozen 2" marshmallows or 8 dozen 1" marshmallows.