Pulse flour, salt, and sugar in bowl of a food processor. Add butter, and process for about 10 seconds. Gradually add ice water until the dough holds together without being wet or sticky - do not process more than 30 seconds. Squeeze dough to test - add additional water if it is crumbly.

Divide the dough in half, then wrap each half in plastic wrap, and use a rolling pin to flatten each ball into a disk. Chill until needed.

Preheat oven to 375. On a lightly floured work surface, roll out dough out to a circle about 1/4" thick. Fit dough into a 9-inch pie plate, and trim crust to a 1/2-inch overhang. Fold under and crimp edge as desired, then brush with beaten egg. Prick crust with fork. Chill until firm.

Fill pie shell with pie weights, and bake until edges of crust just turn golden, about 15 to 20 minutes. Remove pie weights. Return crust to oven, and continue baking until completely golden, about another 15 minutes. Allow shell to cool completely.

Reduce oven temperature to 325 degrees.

Place coconut on a rimmed baking sheet and bake, tossing occasionally, until lightly golden, about 10 minutes. Set aside.

Prepare an ice bath and set aside. In a bowl, lightly whisk egg yolks and set aside. In a medium saucepan, whisk together coconut milk, sugar, cornstarch, and salt. Bring to a simmer (do not boil), and cook, whisking constantly, 3 to 4 minutes.

Whisk one quarter of milk mixture into the egg yolks, then whisk in the remaining milk mixture. Strain into a clean saucepan, and cook on medium-high heat, whisking constantly, until custard is thick, approximately 2 to 3 minutes.

Transfer custard to a medium bowl, and cover with plastic wrap, pressing it directly onto surface to prevent it from skinning over. Place in the ice bath until completely chilled, 30 to 35 minutes.

Melt chocolate. Using a pastry brush, coat the inside of the cooled crust with the melted chocolate. Refrigerate until chocolate is firm. Fill crust with coconut custard and spread evenly.

Chill the bowl of an electric mixer and a whisk attachment. Combine cream and confectioners' sugar in the chilled bowl and beat until soft peaks form.

Spread whipped cream on top of custard. Refrigerate pie several hours before serving. Garnish with coconut and chocolate just before serving.