First, carefully cut your young coconuts in half and save all the coconut water by straining it into a clean bowl. You'll need this water later.
Using your coconut grater (kudkuran), grate all the coconut meat into long, thin strips. Try to keep the strips even in size so they'll cook uniformly. Set these strips aside.
Heat your wok or heavy pan over medium heat (around 350°F/180°C). Add just a small amount of oil, enough to coat the bottom of the pan. Add your coconut strips and cook them until they turn slightly golden brown, stirring often so they don't burn. Once lightly toasted, remove them from the heat and set aside.
In the same wok, combine 1 cup of your saved coconut water with the brown sugar. Turn the heat to high and bring it to a boil, then reduce to medium heat. Let it cook until it becomes thick like syrup (about 10-15 minutes).
While the syrup is cooking, mix your cornstarch with ¼ cup of the remaining coconut water in a small bowl. Stir until there are no lumps. Set this mixture aside.
Once your syrup is thick, return your toasted coconut strips to the wok and stir everything together. Pour in your cornstarch mixture and keep cooking over medium heat. Stir constantly to prevent sticking. You'll know it's ready when you can scoop up some mixture and it holds its shape firmly (about 10-15 minutes).
Reduce the heat to low. Using a spoon, scoop out portions of the mixture and place them on wax paper. Shape each portion into a circle while it's still warm. You can wet your hands slightly to prevent sticking if needed.
Let your bukayo cool completely at room temperature. This will take about 1-2 hours. Once cooled, they should be firm but still slightly chewy.
Store your bukayo in an airtight container at room temperature for up to a week, or in the refrigerator for up to two weeks. If they get too hard, just warm them briefly in the microwave for 5-10 seconds before eating.
Remember: If at any point your mixture becomes too dry while cooking, you can add a little more coconut water, one tablespoon at a time. If it's too wet, just cook it a bit longer until it reaches the right consistency.