Place shredded coconut meat in a heavy saucepan. Add enough water to coconut juice to make 1 1/2 cups of liquid. Add to coconut meat. Simmer mixture over medium heat until coconut is tender, about 10 minutes.
Mix cornstarch with 1/4 cup water. Add cornstarch mixture, condensed milk, and sugar to coconut mixture. Cook over medium heat, stirring constantly, until thickened. Pour mixture into pastry-lined pie pan. Cover with second pastry. Seal edges and cut steam vents in top.
Bake in preheated oven for 30 minutes, until crust is golden brown.