In a food processor, combine flour, butter, salt, and sugar; pulse until mixture resembles coarse meal. Add milk, 1 tablespoon at a time, and pulse, just until mixture forms a ball. Remove dough from machine and flatten. Cover with plastic wrap and refrigerate at least 1 hour. ( If you don't have a food processor you can use your fingers and/or a fork to combine the above mixtures, it will just take a little longer to do it.)
Preheat oven to 375 degrees.
Roll out dough on a floured surface into a 12-inch circle; carefully lift rolled out dough into a 9-inch pie pan. Trim the edges to extend about an inch over the sides of the piepan. Fold overhang under and crimp edges decoratively, using your fingers. Line dough with foil and add pie weights or about 1 to 1 1/2 cups dried beans or rice (to hold crust to pan).
Bake 12 to 15 minutes. Carefully remove weights and foil; return pan to oven and bake until golden brown, about 9 more minutes. Remove and let cool on a rack.
Scald milk in a small saucepan. In a medium bowl, beat eggs lightly; add sugar and salt, and slowly stir in hot scalded milk. Mix in vanilla and coconut.
Pour mixture into baked pastry shell. Sprinkle with nutmeg. Increase oven temperature to 425 degrees and bake on lower rack about 30 minutes, until custard is firm. Refrigerate until chilled, about 4 hours.