Make the crust: Pulse the flour, coconut and salt in a food processor until the coconut is finely chopped. Add the butter and shortening and pulse until the mixture looks like coarse meal with pea-size bits of butter. Drizzle in 3 tablespoons ice water and pulse until the dough begins to come together (add more water, 1/2 tablespoon at a time, if necessary). Turn out onto a sheet of plastic wrap and pat into a disk. Wrap tightly and refrigerate until firm, at least 1 hour and up to 1 day.
Preheat the oven to 375 degrees F. Roll out the dough into an 11-inch round on a lightly floured surface. Ease into a 9-inch pie plate. Fold the overhanging dough under itself and crimp the edges with your fingers. Pierce the bottom all over with a fork. Refrigerate the crust until firm, about 15 minutes. Line the crust with foil, then fill with pie weights or dried beans. Bake until the edges are golden, 20 to 25 minutes. Remove the foil and weights and continue baking until golden all over, 10 to 15 more minutes. Transfer to a rack and let cool completely.
Meanwhile, make the filling: Heat 1 1/2 cups milk and the macadamia nuts in a medium saucepan over medium heat (do not boil). Whisk the egg yolks, 1/2 cup sugar, the cornstarch, vanilla and the remaining 1/4 cup milk in a bowl until combined. Gradually whisk half of the hot milk mixture into the egg mixture, then pour back into the saucepan with the remaining milk mixture and cook, stirring constantly with a wooden spoon, until the mixture thickens and just begins to boil, 2 to 3 minutes. Remove from the heat and stir in the white chocolate until smooth. Transfer the filling to a large bowl and let cool to room temperature, stirring occasionally, about 30 minutes.
Once the filling is cool, bring a few inches of water to a simmer in a medium saucepan. Whisk the egg whites and the remaining 1/4 cup sugar in a large heatproof bowl. Set the bowl over the pan (do not let the bowl touch the water) and whisk until the sugar dissolves and the mixture is warm. Remove the bowl from the pan and beat with a hand mixer until the egg whites are glossy and stiff, about 5 minutes. Fold the beaten egg whites into the filling, then spread in the prepared crust. Cover loosely with plastic wrap and refrigerate until set, at least 6 hours or overnight.
Just before serving, make the whipped cream for topping: Beat the heavy cream and confectioners' sugar with a mixer until medium peaks form. Transfer to a piping bag fitted with a star tip and pipe around the edge of the pie. Top with the macadamia nuts and toasted coconut.