Special equipment: One 9-inch pie pan
Prepare and chill the dough.
Set a rack at the middle level of the oven and preheat to 350 degrees.
Use a large nail or an ice pick to puncture one of the three eyes on the coconut (only one can be punctured so you will need to try each until you find it). Drain the coconut milk out over a bowl. Strain it to remove any flecks of shell and reserve it.
Place the coconut on the oven rack and bake it until it cracks, about 10 to 15 minutes.
Remove the coconut from the oven and let it cool slightly. Remove shell (it will come away easily), then cut the coconut meat into 8 or 10 pieces. With a vegetable peeler, remove brown skin. Coarsely grate 1 cup coconut, either by hand or in the food processor, and reserve it for the filling. Process the remaining coconut until it is very fine.
In a large saucepan over low heat, scald the milk until there are bubbles around the edges. Add the finely processed coconut. Remove from the heat and allow the mixture to cool completely. Pour it through a fine strainer into a bowl; press coconut to extract as much moisture as possible.
In 3 or 4 batches, place coconut in the corner of a clean dish towel and wring out over bowl to extract all remaining liquid. (If you wish, you can toast the wrung out coconut, though it will have very little flavor remaining after soaking in the milk.) Measure the coconut flavored milk and add more milk, if necessary, to make 2 cups. (This may be done earlier in the day or even the day before and set aside tightly covered in the refrigerator.) Pour into a bowl and whisk in sugar, eggs, vanilla and nutmeg and the reserved coconut milk. Stir in the reserved coarsely grated coconut.
Set a rack in the lowest level of the oven and preheat to 350 degrees. Roll out the dough for the bottom crust and arrange in pan.
Pour filling into pie crust. Bake the pie for about 45 minutes, until the crust is baked through and the filling is set, but not over-cooked. After the pie has baked for 30 minutes, check it frequently so it does not over-cook. Once the pie is wobbly textured when the pan is gently shaken, remove it from the oven; it will continue to cook for a few minutes longer after it is removed from the oven. If the pie is over baked, it will be heavy and watery. Cool the pie on a rack.
To mix the dough by hand, combine flour, sugar, salt and baking powder in a medium mixing bowl and stir well to mix. Cut butter into 1-tablespoon pieces and add to dry ingredients. Toss once or twice to coat pieces of butter. Then using your hands or a pastry blender, break the butter into tiny pieces and pinch and squeeze it into the dry ingredients. Occasionally reach down to the bottom of the bowl and mix all the ingredients evenly together. Continue rubbing the butter into the dry ingredients until the mixture resembles a coarse-ground cornmeal and no large pieces of butter remain visible. Beat the egg(s) in a small bowl and pour over the flour and butter mixture. Stir in with a fork until the dough begins to hold together, but still appears somewhat dry. Scatter a teaspoon of flour on the work surface and scrape the dough out onto it. Press and knead the dough quickly 3 or 4 times, until it is smooth and uniform.
To mix the dough in the food processor, combine flour, sugar, salt and baking powder in work bowl fitted with metal blade. Pulse 3 times at 1-second intervals to mix. Cut butter into 1 tablespoon pieces and add to work bowl. Process, pulsing repeatedly at 1-second intervals, until the mixture is fine and powdery, resembles a coarse-ground cornmeal and no large pieces of butter remain visible, about 15 pulses in all. Add the egg(s) to the work bowl and pulse ten times or so, until the dough forms a ball. Scatter a teaspoon of flour on the work surface and scrape the dough out onto it. Press and knead the dough quickly 3 or 4 times, until it is smooth and uniform. Press the dough into a disk (two equal disks for the larger amount of dough). Sandwich the disk(s) of dough between two pieces of plastic wrap and press it into a 6-inch circle. Refrigerate the dough until firm, or until you are ready to use it, at least 1 hour.
Storage: Keep the dough in the refrigerator up to two days, or freeze it double-wrapped in plastic. Because the dough is thin, it will defrost quickly at room temperature when you intend to use it.
Variations: OLD FASHIONED CUSTARD PIE: Omit coconut. Add 1/2 cup heavy or light cream to the milk. Mix sugar with 1 teaspoon cornstarch before adding to milk. Bake as above. SPICE CRUST: Add 1/2 teaspoon ground cinnamon and 1/4 teaspoon each freshly grated nutmeg and ground cloves to the dry ingredients before mixing in the butter. Double the quantities for the 2-crust recipe.
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