Combine gelatin and 1/2 cup ice cold water in a stand mixer with whisk attachment.
Add remaining water, peppermint dark chocolate, corn syrup, sugar, and salt to a small pot. Bring to a simmer over medium-high heat.
Clip a candy thermometer to the pot and continue cooking until the mixture is 240°F. Immediately remove from heat.
Start the stand mixer on low and slowly pour chocolate syrup in while mixer is running. Once all the syrup is added, increase the mixer to high speed and whip for 12-15 minutes until thick and lukewarm.
Whisk cocoa powder and cornstarch together in a small bowl.
Generously grease or spray the bottom and sides of a 9x13 pan. Add about half of the cocoa mixture and shake to coat bottom and sides evenly. Pour any extra powder back into the small bowl.
Pour the marshmallow mixture into the 9x13 pan and smooth the surface. Press crushed soft peppermints into the top then lightly dust with cocoa mixture, saving the remaining powder for later.
Let the marshmallows rest uncovered at least 4 hours or overnight.
Turn the marshmallows onto a cutting board. Dust a knife or pizza cutter with cocoa mixture and cut marshmallows into 1-inch squares. Toss marshmallows with remaining powder and store in an airtight container.