To dissolve the gelatin:.
In a large mixing bowl, add water, vanilla and peppermint extract - sprinkle gelatin over the mixture to bloom and set aside.
To prepare the sugar syrup:.
In a medium to large heavy saucepan, combine sugar, corn syrup, water, and salt. Cover saucepan and bring to a boil over medium to medium-high heat - uncover and allow to cook, without stirring, until it reaches 240 degrees (soft-ball stage).
Place the mixing bowl with the bloomed (softened) gelatin onto the stand mixer, with the whisk attachment in place, and turn the speed to medium. Carefully pour the hot syrup gradually down the side of the bowl - keep the speed around medium so the mixture doesn't splash out of the bowl. When all of the syrup has been added, increase speed to high and beat until the mixture is very fluffy and stiff, but still pourable, about 8-10 minutes.
When the marshmallow mixture is ready, scoop it into a 10" x 15" baking pan lined with parchment paper and coated with nonstick spray. Quickly dribble food coloring all over the top and use a sturdy wooden skewer or toothpick to swirl the color into the marshmallow. Set the pan aside until the mixture firms up, at least 8 to 10 hours.
Before cutting, sift together equal parts confectioners' sugar and potato starch. I used roughly 1/3 cup of each.
Dust the top of a cutting board with the confectioners' sugar mixture - turn the marshmallows out onto the cutting board and peel away the parchment paper. Dust the marshmallow slab all over with the confectioners' sugar mixture. Using a thin, sharp knife, slice the marshmallow into the desired size and shape. Dip all cut edges in confectioners' sugar mixture, shaking off any excess, to keep the marshmallows from sticking.
Makes several dozen depending on the size they are cut into.