In a large bowl or the bowl of a stand mixer, mix the gelatin into ½ cup of the cold water. Let the gelatin sit and dissolve while you cook the other ingredients.
Prepare a 9x9 or 8x8 baking dish by lining with plastic wrap and spraying lightly with cooking spray, then dusting with powdered sugar.
In a medium sauce pan, whisk together the remaining ½ cup water, sugar, corn syrup, and salt. Heat over medium heat until the sugar is dissolved, then increase the heat to medium high. Using a candy thermometer for accuracy, heat the mixture to 240 degrees, then remove from heat.
With the whisk attachment on your stand mixer, turn the speed on low and slowly and carefully pour the corn syrup mixture into the gelatin mixture. (You could also do this with a handheld mixture, just have an assistant nearby to help you pour the hot mixture, and be sure to keep the speed low.) Add the peppermint extract and increase the speed to medium. Beat on medium until the mixture is light and fluffy like marshmallow cream.
Spread about half of the marshmallow mixture in the prepared pan. Add some dots of food coloring (if using) and swirl them through the mixture using a knife or a toothpick. Pour the remaining marshmallow mixture on top and repeat the steps with the food coloring. Sprinkle powdered sugar over the top of the marshmallows and cover. Let sit 6-8 hours or overnight to cool completely before slicing.
When the marshmallows are ready to slice, use a pizza cutter to cut the marshmallows into squares. Toss lightly with powdered sugar (I like to just add them to a zipper bag with a little powdered sugar and shake them around). Store in an airtight container for up to two weeks.