In a food processor, combine the flour, baking powder and salt. Add the butter and pulse a few times, until it forms pea-sized pieces. Add the water and pulse just until the dough starts coming together. Add more water as needed. Remove the dough from the food processor and form into a disc.
On a floured work surface, roll the dough to form a circle about 1/8 inch (3 mm) thick. Line a 9-inch (23 cm) glass pie dish with the circle of dough. Remove the excess dough around the edges, leaving a 1/2-inch (1.5 cm) overhang. Crimp the overhang of dough in a series of curves to make a decorative pattern. Refrigerate for 30 minutes.
With the rack in the middle position, preheat the oven to 375°F (190°C). Cover the dough with foil and fill with dried peas or ceramic pie weights.
Bake for 15 minutes. Remove the peas and foil. Bake for another 10 minutes or until the dough is lightly golden. Let cool completely on a wire rack.
In a small pot off the heat, whisk together the sugar and cornstarch. Add the egg and egg yolks. Mix well. Add the coconut milk, milk, 1 cup (120 g) of shredded coconut and the vanilla. Bring to a boil over medium heat, stirring constantly and scraping the bottom and sides of the pot, until the mixture thickens. Remove from the heat. Pour into the cooled crust.
Cover with plastic wrap directly on the surface of the cream. Let cool and refrigerate for 4 hours or until completely chilled.
In a small skillet, toast the remaining shredded coconut for 2 minutes or until golden. Let cool completely.
In a bowl, whisk the cream, icing sugar and vanilla with an electric mixer until firm peaks form. Garnish the pie with the whipped cream and sprinkle with the toasted coconut.