1. Preheat the oven to 325, place the coconut in a small baking or cake pan, and toast it in the oven until golden brown. The secret to good toasted coconut is consistent browning, so be sure to stir it every 2 minutes until it is an even golden color. It will probably take 8-10 minutes, but monitor your coconut carefully. Once toasted, remove the coconut from the oven and set it aside to cool.
2. Prepare a 9x13 pan by spraying it with nonstick cooking spray, and sprinkle about a cup of the toasted coconut in an even layer on the bottom of the pan, so that the bottom of the pan is covered with coconut.
3. Combine the granulated sugar, corn syrup, and Â¾ cup water in a large pot over medium heat. Stir until the sugar is completely dissolved, then stop stirring and allow the mixture to come to a boil. Continue boiling until mixture reaches 260 degrees (hard-ball stage). This process will take a while, so move on to the next two steps while the sugar syrup cooks, but be sure to check the sugar syrup frequently so that it does not go above 260 degrees.
3. While the sugar syrup cooks, prepare the gelatin mixture. In a small saucepan, combine 3/4 cup water and the coconut extract. Sprinkle the gelatin over the top and stir briefly. Let the gelatin sit for 5 minutes, until it is completely absorbed by the liquid. Set the pan over low heat and stir constantly until the mixture is liquid.
4. While the sugar syrup is boiling and the gelatin is softening, place the room temperature egg whites in the clean bowl of a large stand mixer fitted with the whisk attachment. Once the sugar syrup nears 245 degrees, begin to beat the egg whites. Beat them until they hold firm peaks, but do not overbeat or they will be crumbly. If the egg whites are ready before the sugar syrup reaches the correct temperature, stop the mixer until the sugar syrup is ready.
5. Whisk the gelatin mixture into the sugar syrup. This mixture now needs to be poured into the egg whites. If your saucepan has a spout you can pour it from the saucepan, but if it does not I recommend pouring the syrup into a large measuring cup or pitcher so that it is easier to pour. The sugar syrup is very hot and it can cause painful burns if it accidentally spills or splatters. With the mixer running on low, carefully pour the hot syrup in a thin stream into the egg whites. Once all of the sugar syrup is poured, turn the mixer to medium-high. Continue to beat the marshmallow in the mixer until it is thick enough to hold its shape and is completely opaque. Depending on your mixer, this will take about 5-10 minutes.
6. Pour the marshmallow mixture into the prepared pan and smooth the top flat with an offset spatula. Immediately sprinkle another cup of the toasted coconut on top of the marshmallow in an even layer. The remaining coconut will be used to coat the sides of the marshmallow squares when they are cut later, so set it aside for now. Allow the marshmallow to set for at least 6 hours, or overnight.
7. Once the marshmallow has set, itâ€™s time to cut it into squares. Lift the marshmallow from the pan using the foil as handles, and flip it facedown on the prepared surface. Peel the foil off the top of the marshmallow. If the top is sticky, sprinkle it with a little more of the toasted marshmallow.
8. Spray a large, sharp chef's knife with nonstick cooking spray. Cut the marshmallow block into small 1" squares, or whatever size marshmallows you desire. You can also use sharp metal cookie cutters to cut different shapes out of the marshmallow. Dredge the cut edges of the marshmallows in the remaining toasted coconut so that they are not sticky. Your marshmallows are now ready to eat! They are best soon after they are made, but if your environment is not too humid, you can store them up to three days in an airtight container at room temperature. You may need to dredge the sides in toasted coconut again if they get too sticky.