In a small pot, add water and cinnamon sticks, bring to a boil and cook for 10 minutes. Set aside and discard cinnamon sticks.

Place the rice and the cinnamon water in a large saucepan, over medium heat and cook for 5 minutes.

Add salt, butter, 1 cup milk, coconut extract, 1 cup coconut milk and sugar. Stir well to mix and cook uncovered for approximately 15 to 20 minutes.

Reduce heat to medium-low. Add the remaining coconut milk, heavy cream and condensed milk. Stir with a wooden spoon. Cook for 1 hour and 15 minutes, or until the rice pudding thickens to desire consistency. Add the coconut flakes.

Stir well and remove from heat, and let it cool at room temperature. The consistency should be very creamy. Divide the rice pudding evenly into 6 ramekins. Refrigerate for a least 1 hour or overnight.

Just before serving, preheat the broiler and top each ramekin with 1 tablespoon of brown sugar. Put the ramekins in a baking pan filled with water and broil the custard for 2 minutes, or until golden brown. Serve and Enjoy!