Preheat oven to 325°. Spread flaked coconut on a baking sheet and bake until golden brown, 6 to 8 minutes.
Oil an 8-in.-square baking dish. In a small bowl, stir together 1/2 cup coconut milk and cornstarch until smooth.
In a medium nonstick saucepan, combine 1 1/2 cups coconut milk (if you don't have enough, augment with water) and sugar. Stir over medium heat until sugar has dissolved. Drizzle cornstarch mixture slowly into saucepan, whisking, and whisk in vanilla and salt. Cook, whisking vigorously (do not allow to boil), until mixture is very thick, pulling away from pan, and no longer tastes floury, 4 to 6 minutes. Pour into prepared dish and spread evenly. Let cool briefly, then cover with plastic wrap and chill until set, at least 1 hour.
Cut haupia into 22 to 24 triangles and sprinkle each with a pinch of toasted coconut.