Step 1

For the pie crust: Pulse the flour, sugar, and salt in a food processor fitted with the metal blade until combined. Add the butter and pulse until it resembles yellow cornmeal mixed with bean-size bits of butter, about 10 times. Add the egg and pulse 4 to 5 times until the dough forms a ball. (If the dough is very dry add up to a tablespoon more of cold water.)

Step 2

Transfer the dough to a work surface. Form the dough into a disk, wrap with plastic wrap and refrigerate until thoroughly chilled, at least 1 hour.

Step 3

Roll the dough on a lightly-floured surface into a 12-inch circle about 1/8-inch thick. Transfer the dough to a 9-inch pie pan and trim the edges, leaving about an extra inch hanging over the edge. Tuck the overhanging dough underneath itself to form a thick edge that is even with the rim. Flute the edge as desired. Freeze the pie shell for 30 minutes.

Step 4

Arrange a rack in the center of the oven and preheat to 400 degrees F. Put a piece of parchment paper or foil over the pie shell and fill with dried beans or pie weights. Bake on a baking sheet on the center rack until the dough is set, about 20 minutes. Remove from the oven and lift the sides of the parchment to remove the beans. Continue baking until the pie shell is lightly golden brown, about 10 more minutes. Cool on a wire rack.

Step 5

For the filling: Whisk together the egg yolks, 1/4 cup of the milk and the cornstarch in a medium bowl until smooth and well combined. Stir together the remaining 3/4 cup milk, the half-and-half, sugar and kosher salt in a large saucepan. Heat over medium heat until barely simmering. Temper the egg yolks by slowly pouring the hot milk and cream into the egg yolks while continuing to whisk. Pour the custard back into the pan and place over medium-low heat. Cook, stirring constantly, until the custard is very thick and smooth, about 5 minutes; it will be the consistency of a pudding. (If the filling has scrambled a bit, or doesn't look smooth, strain it through a fine-mesh sieve into a separate bowl before adding the coconut.) Stir in the butter until melted, then stir in the vanilla and shredded coconut. Spread the filling into the cooled pie crust. Place plastic wrap directly on the surface of the pie and refrigerate until chilled, about 2 hours, but preferably overnight.

Step 6

For the meringue: Add the egg whites, sugar, cream of tartar and kosher salt to the bowl of a stand mixture fitted with the whisk attachment and whisk to combine. Place the bowl over a saucepan of simmering water, making sure the bottom of the bowl does not touch the water. Cook, whisking constantly, until the sugar dissolves and the mixture feels very hot to the touch. Transfer the bowl to the mixer and add the vanilla. Whisk on medium-high speed until stiff peaks form, 5 to 6 minutes.

Step 7

Remove the plastic wrap from the pie and gently mound the meringue on top of the filling. Use an offset spatula to completely cover the filling and meet the crust all around the edges. (This will completely seal in the filling and help prevent weeping.) Use the offset spatula to form swirls and peaks in the meringue. Toast the meringue using a kitchen torch or broil in the oven until golden brown, keeping an eye on the meringue if broiling. Sprinkle all over with toasted coconut and serve.