Preheat the oven to 350 degrees Fahrenheit. Line two nine-inch cake pans with circles of Gefen Parchment Paper.

In a mixing bowl, whisk together the flours and dry ingredients.

Add in eggs, oil, coconut milk, lime juice, and vanilla. Beat until smooth. The mixture should resemble a slightly thick and sticky cake batter.

Scoop the cake batter into the two prepared cake pans and spread evenly. Use wet hands, if necessary, to smooth out the tops.

Bake in the center of the oven, side by side, for 30 minutes or so, until firm and springy. A cake tester inserted into the center should emerge clean. Cool on a wire rack.

While the cakes bake, make the frosting. In a mixing bowl, beat the shortening and extract until combined.

Add in sugar and half the coconut milk and beat until smooth. Slowly add remaining coconut milk, as you need it, a little at a time, until you achieve a smooth and creamy consistency.

When the cakes are cool, gently remove one from the pan and peel off the parchment paper. Trim off the domed top if you like, using a long serrated knife, to keep the cake layer even. Brush off any crumbs.

Center the first layer top-side down on a cake plate. Frost the layer with roughly 3/4 cup of icing.

Remove the second cake layer from its pan and peel off the parchment paper. Trim the dome top, if you like (brush off any crumbs). Place this layer on top of the frosted layer and scoop about a cup of frosting onto the top of the cake and spread it evenly to the edges.

Begin adding frosting to the sides of the cake, spreading it evenly over the sides. Clean the frosting spatula under warm water and dry it off.

Smooth the sides by turning the plate as you hold the spatula firmly in place. Clean off the spatula with warm water again, dry it, and smooth out the top.

Sprinkle with flaked sweetened coconut, if desired.

Allow the frosting to set, or chill briefly before covering and storing the cake.