Coconut patties are a traditional West Indian pastry. If using grated coconut, begin with step two.
Preheat oven to 350 degrees. Use an ice pick or screwdriver to poke holes in the "eyes" of the coconut, and drain milk. Reserve milk for another use. Place coconut in the oven for 15 minutes. Wrap in a cloth towel, and hit with a hammer to crack open. Remove coconut from hard outer shell; discard shell. Use a vegetable peeler to remove thin brown coating from coconut. Grate coconut on the large holes of a box grater to yield 4 cups.
Combine grated coconut, brown sugar, nutmeg, and water in a medium saucepan; cook over medium-low heat, stirring until sugar has melted and coconut is thoroughly coated, 3 to 5 minutes. Transfer to a bowl, and add butter, stirring until it is melted. Cool to room temperature.
Lightly dust a clean work surface with flour, and divide dough into 2 pieces. Roll each piece to 1/8 inch thick. Use a 3 1/2-inch-round cutter to cut out disks. Reroll scraps; cut additional disks.
Make an egg wash by combining egg and cream in a small bowl. Place 1 generous tablespoon coconut filling on each disk. Apply a light coating of egg wash to edges using a pastry brush. Fold into half-moon shapes, and press edges together with the tines of a fork to seal.
Place patties on a baking sheet lined with a Silpat (a French nonstick baking mat) or parchment paper. Bake for 20 to 25 minutes, until golden brown. Transfer to a wire rack to cool.
These patties can be formed a day ahead and kept in the refrigerator. They are best eaten the day they are baked.