In a food processor, add the flour, salt, and butter and pulse until the butter is broken up into small bits.

Add the water and pulse until the mixture looks like crumbled dough.

Transfer to an unfloured work surface. Gather and shape into a flat disc.

Lightly dust the work surface with flour and roll out the dough into a 12-inch (30 cm) round.

Transfer to a 9-inch (23 cm) pie plate. There should be some overhanging dough. Tuck this excess under itself, all the way around, and pinch and shape into an evenly raised border, using the flat lip of the pie plate as a base.

Flute or crimp the crust. Prick the dough all over with a fork. Refrigerate for at least 30 minutes and up to overnight.

Preheat the oven to 350°F (180°C). Set the pie plate on a sheet pan and line the pastry with foil so it covers the dough entirely. Fill with dried beans or pie weights.

Bake until the perimeter is matte and light golden, 20 to 25 minutes.

Remove the foil and beans and continue to bake (on the sheet pan) until the crust is golden brown all over, 10 to 15 minutes.

Transfer the pie plate to a wire rack and let cool 15 minutes.

In a large bowl, using an electric hand mixer, beat the eggs, ube halaya, coconut milk, granulated sugar, salt, vanilla extract, and ube extract until smooth, about 1 minute.

Pour into cooled crust.

Bake until edges of the filling are set but the center still jiggles slightly, 55 to 65 minutes. (Filling will puff as it bakes but will settle as it cools.)

Transfer to a wire rack and let cool at least 2 hours. Pie can be served slightly warm or room temperature.