Cake:

Butter and lightly flour the cake pans.

Preheat the oven to 350°.

Cream together the butter and sugar in the bowl of an electric mixer.

One at a time, add the egg yolks and mix until blended.

Sift together the flour, baking powder, and salt, and add alternately with the coconut milk.

Stir in the lemon zest.

In another bowl, beat the egg whites until stiff and glossy. Fold the whites into the batter with a rubber spatula.

Divide the batter equally between the cake pans and bake for 40 minutes, or until the cake pulls away from the sides of the pan.

Remove the cake pans and cool on wire racks.

Lemon filling:

In a medium non-aluminum saucepan, bring the lemon juice, sugar, and 1 cup water to a boil.

In a bowl, dissolve the cornstarch in 1/3 cup water and mix in the yolks.

When the lemon syrup boils, remove from the heat and gradually whisk it into the yolk mixture.

Return to the saucepan and bring to a boil.

Remove from the heat and whisk in the butter. Place a sheet of plastic wrap directly on the surface of the filling and set aside.

Seven-Minute icing:

In a large heatproof mixing bowl, combine all of the ingredients.

Set the bowl over a pot of boiling water and beat with an electric mixer for about 7 minutes, until white peaks form.

Remove from the heat and beat until the icing stiffens and becomes spreadable.

Final assembly:

Trim the tops and bottoms of each cake with a serrated knife.

Cut the cakes horizontally in half.

One at a time, spread each layer with the lemon filling, stacking evenly.

Ice the cake with seven-minute frosting.

Cover the tops and sides of the cake with the shredded coconut.