Open the coconut: Heat oven to 375ºF. Place the coconut onto a folded towel set in a large bowl. Find the 3 eyes on 1 end of the coconut and, using a nail or screwdriver and hammer or meat mallet, hammer holes into 2 of the eyes. Turn the coconut upside down over a container and drain the water from the coconut. Store the water in an airtight container in the refrigerator for up to 1 week. Place the coconut onto a half-sheet pan and bake in the oven for 15 minutes. When finished cooking, the coconut should have cracked in several places. Using an oyster knife or other dull blade, separate the hard shell from the brown husk. Using a serrated vegetable peeler, peel the brown husk from the coconut meat. Rinse the coconut meat under cool water and pat dry. Break the meat into 2- to 3-inch pieces. With the grater disk attached to a food processor, grate the coconut.
For the milk: Place 1/2 cup of the coconut into a small mixing bowl and pour over the boiling milk. Stir to combine. Cover tightly and allow to sit for 1 hour. Transfer the mixture to the carafe of a blender and process for 1 minute. Place a tea towel over a mixing bowl and carefully pour the mixture into it. Gather up the edges and squeeze until all of the liquid has been removed. Discard the coconut. You may use the milk immediately or store in the refrigerator for up to 2 days.
For the cream: Repeat the same procedure as above, using the remaining 1 cup of freshly grated coconut.