Coconut Custard Pie

Ingredients:
2 cups all-purpose flour
1 teaspoon salt
1 1/2 sticks (3/4 cup) plus 3 tablespoons cold unsalted butter
4 to 6 tablespoons ice water
5 large eggs
3/4 cup plus 2 tablespoons sugar
2 cups whole milk
1/2 cup half-and-half
1 teaspoon vanilla
1/4 teaspoon salt
1 cup sweetened flaked coconut
1/2 cup fresh coconut shavings (cut with a vegetable peeler from a shelled coconut) or sweetened flaked coconut
1 cup chilled heavy cream
2 tablespoons sugar
1/2 teaspoon vanilla
pie weights or raw rice

Instructions:
Whisk together flour and salt in a large bowl. Cut 6 tablespoons butter into 1/2-inch cubes, then blend into flour with your fingertips or a pastry blender until mixture resembles coarse meal. Cut another 6 tablespoons butter into 1/2-inch cubes, then blend into flour in same manner until mixture has small (roughly pea-size) butter lumps.
Drizzle evenly with 4 tablespoons ice water and gently stir with a fork until incorporated. Squeeze a small handful: If it doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring until just incorporated, then test again. (Do not overwork mixture, or pastry will be tough.) Gather dough into a ball in bowl, then flatten into a 5-inch square on a sheet of wax paper. Wrap dough in wax paper and chill 30 minutes.
Cut remaining 3 tablespoons butter into very thin slices. Roll out dough on a floured surface with a floured rolling pin into a 13- by 11-inch rectangle (1/3 inch thick). Arrange dough with a short side nearest you and place butter slices evenly over dough, then fold dough into thirds like a letter: bottom third up and top third down over dough.
Turn dough so a short side is nearest you and roll dough into a 13- by 11-inch rectangle (1/3 inch thick) again, then fold dough into thirds like a letter once more. Brush off any excess flour, then wrap dough in wax paper and chill at least 3 hours.
Preheat oven to 375°F.
Roll out dough on floured surface with floured rolling pin to a rough 16-inch square, then fit into a 10-inch (6-cup) glass pie plate. Trim excess dough, leaving a 1-inch overhang, then fold overhang under to form a rim (baked crust will not hold a crimp). Line pie shell with foil and fill with pie weights. Bake in middle of oven until edge of pastry is set and pale golden, 17 to 20 minutes.
Carefully remove foil and weights, then prick bottom and side of pie shell all over with a fork. Bake, pricking again if any large air pockets form, until pie shell is golden all over, about 15 minutes more. (Leave oven on.)
Beat eggs in a large bowl with an electric mixer at medium speed until combined well. Beat in sugar, milk, half-and-half, vanilla, and salt, then stir in flaked coconut.
Pour custard into hot pie shell and cover edge of pie with a pie shield or foil (to prevent overbrowning). Bake in middle of oven until custard is set 2 inches from edge but still jiggles slightly in center, 30 to 40 minutes. (Leave oven on.) Cool pie completely on a rack, about 1 1/2 hours.
Reduce oven temperature to 350°F.
Spread coconut shavings in a shallow baking pan and bake in middle of oven, stirring once, until pale golden, about 5 minutes (watch carefully, since coconut burns easily). Cool in pan on rack.
Just before serving, beat cream with sugar and vanilla in a bowl with cleaned beaters at medium speed until it just holds soft peaks. Spread cream over pie and sprinkle with toasted coconut.