Begin by cutting about 1 1/2 inches off the top of each sugar cone. Hold the cone against a cutting board, and using a sharp serrated knife, gently saw through the cone. Try not to use much pressure or press down hard—it’s easiest if you let the sawing motion do all the work. Trim off any edges that are terribly uneven. It’s okay if they’re not perfect—the sprinkles will disguise any mistakes.
Melt the candy coating in the microwave. Use a pastry brush to brush a thin layer of coating around the top edge of one of the cones, then while the coating is still wet, dip it in the sprinkles until it’s covered. Set aside and repeat until all of the cones have a layer of sprinkles around the top. An alternate method is to dip the top of the cones in the coating and then the sprinkles, but I found that this gave a thick layer of coating that tasted and looked a little thick for my taste.
Use a sharp knife or a razor blade to cut 24 small X’s in the top of the cardboard box. Push the bottom of a cone into each X, so that the box acts as a stand holding the cones upright. Set aside for now.
To make the marshmallow, place the room temperature egg whites in the bowl of a large stand mixer fitted with a whisk attachment.
Pour the strawberry puree in a small bowl, and whisk in the gelatin. Set the bowl aside to let the gelatin "bloom," or absorb the puree.
Pour the 1/2 cup of water in a medium heavy-bottomed saucepan, and stir in the granulated sugar, the light corn syrup, and the salt. Place the pan over medium-high heat and continue to stir until the sugar dissolves. Brush down the sides of the pan with a wet pastry brush to remove any stray sugar crystals. Insert a candy thermometer.
Cook the sugar syrup, without stirring, until the thermometer reaches 260° Fahrenheit. This will take 10-15 minutes, so while you're waiting for the sugar to cook, microwave the gelatin bowl for about 20 seconds, until the gelatin liquefies.
When the sugar syrup reaches 245° Fahrenheit, begin beating the egg whites on medium speed. The egg whites should be well-beaten and be able to hold firm peaks at approximately the same time the sugar syrup reaches 260° Fahrenheit. When the sugar syrup is at 260°, remove the pan from the heat and carefully whisk in the liquid gelatin mixture. It will bubble up and steam a bit, so watch your hands during this step.
The hot sugar syrup now needs to be added to the egg whites. If your saucepan does not have a spout, pour the syrup into a large mixing cup or pitcher with a spout, to give you more control over the process. Turn the mixer to low, and with the mixer running, slowly stream the hot sugar syrup into the beaten egg whites. Try to pour the syrup close to the sides of the bowl, so it doesn't hit the whisk and splatter everywhere.
Once all of the syrup is added to the whites, gradually increase the speed of the mixer until it is running on medium-high speed. Whip the marshmallow until it is very thick, shiny, and opaque, about 10 minutes depending on your mixer. When you lift the whisk from the marshmallow, it should slowly stream from the whisk in a thick ribbon. Once the right texture is reached, add 1-2 drops of pink gel food coloring, then mix it in until no streaks remain.
Fit a pastry bag with a star tip. Spoon a little marshmallow into the bag, and practice making a swirl into the bowl of marshmallow. If it starts to droop and doesn’t hold its shape, let the marshmallow sit for about a minute, then spoon a little more into the bag and test it again. It might be a little soft at first, but after just a few minutes it will get firmer, and once it reaches the texture where you can pipe a swirl without it drooping and melting, act quickly! Fill the bag with marshmallow and start piping your marshmallow cones: pipe the cone full of marshmallow, then finish with a big swirl on top of the cone. Repeat until all of the cones are filled with marshmallow. (If the marshmallow gets too stiff to pipe well, you might be able to save it by placing the bowl of marshmallow over a warm water bath and warming it gently and stirring until it loosens.)
Let the marshmallow cones sit for at least 4 hours, until the marshmallow is completely set.