In a large bowl, sift the flour and salt. Cut the chilled butter and margarine into 1-tablespoon bits and add to the flour.
With a pastry cutter, work flour and shortening together until mixture resembles coarse meal.
Add the ice water little by little pressing the pastry together into a ball. Wrap and chill for at least 1 hour.
It is very important to work the pastry as little as possible. Don't over handle. A secret to light, flaky pastry is to keep the mixture cool, add as little water as possible, and mix only as much as necessary.
FOOD PROCESSOR METHOD
Put flour and salt in bowl of machine. Cut butter and margarine into flour. Process a few seconds until mixture resembles coarse meal.
Drop by drop add the water, processing very briefly. The whole process would take 20 to 30 seconds.
Wrap and chill the pastry for at least 1 hour.
Preheat oven to 425 F. If pastry has been chilled for a long time, let it sit at room temperature for at least 15 minutes before rolling.
Lightly flour a pastry board, marble counter, or kitchen counter. Divide the pastry in half. Pat each piece of pastry into a flat round.
Lightly flour the rolling pin. Roll pastry in one direction only, turning pastry continually to prevent it from sticking to the surface.
If you are doing a deep dish pie plate, you could use both pieces of dough (that’s what I did). If not, store second portion of dough wrapped in plastic for another pie.
Using pie plate as a guide, measure rolled-out pastry -- it should be slightly larger than the pie plate and 1/8-inch thick. Fold rolled pastry circle in half so you can lift it more easily.
Unfold, gently fitting the pastry into the pie plate, allowing pastry to hang evenly over the edge. Fold edges over and flute. Line the dough with foil paper and fill the dough with dried beans or pie weights. Bake at 425 for 10 minutes.
Remove the weights and the foil paper and bake another 10 minutes (or until golden). Cool completely on a wire rack.
Decrease the oven temperature to 350 F. Spread 1/2 cup coconut on a rimmed baking sheet. Bake until golden, 10 to 12 minutes, tossing occasionally. Don’ t leave the oven for a minute. Check it constantly because it can go from nicely toasted to badly burned in a matter of minutes.
In a medium saucepan, whisk together the sugar, cornstarch, and salt. Whisk in the milk, and cook over medium-high heat, stirring constantly, until bubbling and thick; about 7 minutes total (you end up cooking it 2 minutes after it comes to a boil.)
In a medium sized bowl, whisk egg yolks until combined.
Add the milk mixture into the egg yolk mixture in a slow and steady stream. Whisk until completely incorporated. Return the mixture to the saucepan and cook over medium-high heat, stirring constantly, until it returns to a boil; about 1-2 minutes.
Strain the mixture through a fine-mesh sieve into a large bowl and stir in 1 1/4 cups coconut (I didn’t strain my mixture and it was perfectly fine). Pour filling into cooled crust and smooth top.
Refrigerate until filling is chilled and completely set, about 2 hours (or wrap tightly with plastic and refrigerate, up to 2 days).
When the filling has cooled for 2 hours, make the Italian meringue.
Add the room temperature egg whites and the cream of tartar to the bowl of a mixer.
Before beating the egg whites and cream of tartar, add the sugar and water to a large sauce pan and bring to a boil.
Let it simmer without stirring it until a candy thermometer reads 250 F. While it is simmering, beat the egg whites and cream of tartar in the mixer for about 3 minutes. When the sugar syrup reaches 250 F carefully pour it into the mixer with the egg whites and beat until it is thick; about another 4 minutes.
The total mixing time is about 7 minutes.
Spread the meringue over the pie filling.
Toss on the toasted coconut before serving. I ended up chilling the pie filling for about 5 hours until it was completely set. I attempted to slice it after 2 hours and it was definitely not ready.