I use Alton Brown's homemade marshmallow recipe as my base. For a 9x13 pan, I actually double the recipe so I can have big, fluffy marshmallows. I like them to be big enough that I just want 1 marshmallow per peppermint schnapps-spiked cup of hot cocoa.
Put down a good layer of cornstarch and powdered sugar in your pan, then heat your sugar syrup and get the gelatin ready in the stand mixer, adding 1-2 teaspoons of peppermint extract to the gelatin (1 teaspoon if you don't want it to be too strong, definitely do 2 if you're doing a double batch).
Once you've drizzled in the gelatin and it's gotten big and fluffy and marshmallow-y, drizzle some red food coloring over the top and fold it in. If you'd rather them be a uniform color instead of marbled, add the food coloring with the gelatin or while the mixture is whipping.
Let sit at least 4 hours, but ideally overnight. As I cut them, I toss them into a big bowl with cornstarch and powdered sugar. It takes a surprising amount of both to keep them from sitting.
Store these in an airtight container and they will last at least until Christmas, probably into January. I've never actually had them mold or anything, but they start to shrivel up after a while.