To make the curd, puree mango, sugar, lime juice and salt in processor or blender.
Add yolks; puree 15 seconds longer.
Pour the mixture into a 2 quart saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly.
The curd will thicken at about 170 degrees F, or just below simmer.
Whisk in butter 1 piece at a time.
Remove from heat, carefully transfer to a glass bowl or jar and cover and refrigerate overnight.
For the Coconut Cake Layers-
Preheat oven to 325°F.
Butter two 8-inch pans or three 9-inch round cake pans. Line with round parchment paper; butter parchment, dust lightly with flour and shake off excess.
Sift together cake flour, all-purpose flour, baking powder and salt.
In a separate bowl, combine unsweetened coconut milk and vanilla; whisk to blend, add coconut and stir to blend.
In a bowl of a stand mixer fitted with a paddle attachment, beat butter and 1½ cups sugar for 3 minutes, or until light and fluffy.
Add eggs, one at a time, and mix until incorporated; transfer batter to a large bowl.
Alternately add flour mixture and coconut mixture to batter in 3 batches, until blended.
In the bowl of a stand mixer fitted with a wire whip, beat egg whites with cream of tartar and 1½ cups sugar to form medium stiff peaks; add to batter, stirring slowly with a balloon whisk until incorporated.
Spread batter evenly in pans; tap pans on counter to eliminate air bubbles.
Bake for 35 minutes, or until a toothpick inserted in center comes out clean; cool on cooling racks for 5 minutes. Run a knife around outer edges of pans and invert cakes onto racks.
To make the Coconut Cream Cheese Frosting, cream cream cheese and butter together until fluffy.
Turn mixer to low and beat in powdered sugar, add coconut extract.
Beat on high for 5 minutes.
To assemble the cake, place cooled cake layer on cake plate.
Pipe a thick ring of frosting along the edge of the cake, then fill with about 1/2 cup of mango curd.
Top with next layer and repeat. Once middle layers have curd, place cake in fridge for 1 hour.
Once set, frost the outside of the cake and garnish with toasted coconut shavings.