Puncture the soft top part of the coconut with a long nail or ice pick and drain liquid into a small dish or measuring cup.
Crack the coconut using a hammer and separate the white meat from the shell. Peel off the thin brown skin; strain the reserved coconut liquid through a fine sieve to remove any impurities. Measure liquid, if there is not ½ cup of liquid additional water may be added to equal ½ cup. Using half the coconut meat (approximately 4 oz weight) puree the coconut with the liquid. This mixture should measure 1 cup approximately.
Grate the remaining coconut with the medium blade of a food processor or on a medium hand grater, reserve ½ cup grated coconut and package the remaining and store in freezer or refrigerator for other uses.
Preheat oven to 300 degrees and butter a 2 quart oven proof casserole.
Add the coconut slurry, half and half, rice, salt and brown sugar; place in preheated oven and bake for 2 hours making sure to stir every 30 minutes to prevent the rice from settling to the bottom.
The last 30 minutes of cooking, stir in the vanilla extract, raisins and ginger. Sprinkle with the reserved ½ cup grated coconut.
While the pudding is cooking, peel and dice mango over blender jar to capture all the juices; add the lime juice and puree together in a blender. Pour into small dish, cover and refrigerate until serving time.
Serve the pudding warm from the oven topped with a spoon or so of the mango puree.