Peel and dice the mangoes into 1-inch chunks and place into a medium-sized saucepan set over medium heat. Add the coconut water, sugar, molasses, mint, and basil and mix well. Cook until the mixture comes to a boil, reduce the heat to a simmer, and cook for about 20 minutes, until the mangoes are completely soft.
Remove from the heat, scoop the mixture into a fine-mesh strainer set over a bowl and press and mash to get all the liquid through. Transfer to a container, cover, and refrigerate for at least 8 hours, until completely chilled.
Place the chilled mixture into an ice cream maker and follow the manufacturer’s instructions. Freeze until solid. This sorbet will keep for 3 weeks.