In a medium saucepan bring the water, 1 cup coconut milk and a pinch of salt to a boil. Add the rice, reduce the heat to low, cover and cook for 25 minutes. Stir frequently.
In the meantime cut the mango. Put it on your cutting board stem end down, place your knife about 1/4 inch from the widest center line (to cut beside the core) and cut down through, then repeat this cut on the other side. Now cut parallel slices into the mango but don't cut through the skin. Turn the mango one quarter and cut another set of parallel slices. Use a large spoon to scoop the mango slices out of the skin.
Puree half of the mango slices with 1/4 cup coconut milk, lime juice, and 1 tbsp of the agave syrup.
In a small pan on low to medium heat toast the shredded coconut without any oil for a few minutes until it becomes golden brown and aromatic. Be careful not to burn the coconut.
When the coconut rice is done turn off the heat and add 2 tbsp agave syrup to the rice. Mix in the toasted shredded coconut and make a taste test. If it's not sweet enough for you add a little bit more agave syrup. Divide the coconut rice between bowls and top with pureed mango. Then add a few of the sliced mango to each bowl.
You can serve my breakfast mango rice pudding warm or cold. If you want to make it in advance just cover the bowls with plastic wrap and keep in the fridge for up to 2 days.