Preheat the oven to 250 degrees. Butter a 9-by-13-inch metal baking pan and line the bottom with wax paper or parchment paper. Butter and flour the paper. In a medium bowl, whisk the cake flour with the baking powder and salt. In a small bowl, whisk the coconut milk with the vanilla and coconut extracts.

In a bowl, using a handheld electric mixer, beat the butter with 1/2 cup of the granulated sugar until fluffy. Add the egg yolks one at a time, beating well between additions. With the machine at low speed, add the dry ingredients in 4 batches, alternating with the coconut-milk mixture.

In a large bowl, using clean beaters, beat the egg whites until soft peaks form. With the machine on, gradually beat in the remaining 1/2 cup of granulated sugar until the egg whites are thick and glossy. Scrape the beaten whites into the cake batter and fold until just combined.

Scrape the batter into the prepared pan and bake for 1 hour and 35 minutes, until a cake tester inserted in the center comes out clean and the cake springs back when lightly pressed. Transfer the cake to a rack and let cool to room temperature.

In a medium saucepan, combine the milk, coconut milk and saffron and bring to a simmer over moderate heat. In a medium bowl, whisk the sugar, cornstarch and salt. Whisk in the egg yolks until smooth. Gradually whisk in half of the hot saffron milk. Scrape the mixture into the saucepan and cook over moderate heat, whisking, until the saffron cream is thickened and just comes to a simmer, 4 minutes. Transfer the cream to a heatproof bowl and stir in the butter. Press a piece of plastic wrap directly onto the surface of the cream and refrigerate.

In a medium bowl, using a handheld electric mixer, beat the cream cheese with the butter until smooth. Add the confectioners' sugar and beat well. Refrigerate until chilled but still spreadable, about 10 minutes.

Unmold the cake and discard the wax paper. Using a large serrated knife, slice the cake in half crosswise to create two 9-by-6 1/2-inch layers. Transfer one layer to a platter and spread the saffron cream on top. Cover with the second cake layer, flat side up. Using an offset spatula, spread the cream cheese frosting all over the top and side of the cake. Press the coconut onto the side of the cake and sprinkle the rest of the coconut on the top. Serve right away or lightly chilled.

The unfrosted cake can be wrapped in plastic and kept at room temperature overnight, or frozen for up to 1 week. The frosted cake can be refrigerated, covered, overnight. Serve at room temperature or lightly chilled.