Place the coconut milk and grated coconut in a blender, and puree until smooth. Set aside.
Place 2 cups of milk in a medium pot and set over medium-low heat. Add the cinnamon sticks, and warm through for 8-10 minutes, or until the milk is slightly steaming.
Add the coconut mixture to the warm milk, and stir to combine. Allow the mixture to warm through, then add the condensed milk, sugar, vanilla, clove (if using) and salt. Stir again.
Increase heat to medium-high, and cook the mixture for another 8-10 minutes, stirring frequently so the milk doesn't stick to the bottom of the pan.
Meanwhile, combine the remaining 1 cup of milk with cornstarch in a small bowl. Whisk until dissolved.
Remove and discard the cinnamon sticks.
Reduce heat back to medium-low, and stir in the cornstarch mixture. Stir continuously for 2-4 minutes, or until the Natilla thickens. Remove from heat, and pour into a loaf pan or small dessert cups. A plastic spatula is useful for getting all of the Natilla out of the pot.
Allow the Natilla to cool at room temperature for 2 hours before serving. Garnish with ground cinnamon and serve with a spoon. Refrigerate unused portions, tightly wrapped, for up to 1 week.
Please note that the nutritional information for this recipe is only an estimate, and has been calculated using a plugin.