Sprinkle gelatin over the water in a small bowl. Stir and let sit for about 20 minutes to bloom.
Combine the granulated sugar, corn syrup, honey, and water in a medium saucepan and bring to a boil over medium heat. Cook without stirring until the syrup reaches 250 F°.
Carefully pour the hot syrup into a stand mixer fitted with a whisk attachment and add the bloomed gelatin. Whip on low speed until the gelatin is completely dissolved. Increase the speed to medium-high and continue to whip for 4-6 minutes. The syrup will turn white and quadruple in volume. When the marshmallow is firm enough to hold a medium-stiff peak, stop whipping.
Using a rubber spatula, place 2 large scoops of marshmallow in a piping bag so that it is ⅓ full. Push the marshmallow down toward the tip of the bag. Cut an opening about 1 inch wide straight across the tip of the bag.
While the marshmallow is still warm, fill each mold about ¾ full. Push a rectangle of ice cream into the center of the marshmallow in each mold, which will cause the marshmallow to push up over the sides of the mold. Pipe in a small amount of marshmallow to cover any exposed ice cream. Using a small offset spatula, level the marshmallow so it is is the exact height of the mold.
After all the molds in the pan have been filled, let them set quickly for 1-2 minutes, Freeze until set, about 2 hours.