1. To prepare cake: Preheat oven to 350 degrees F. Coat two 9-inch round cake pans with cooking spray. Dust lightly with flour, shaking out the excess (or use cooking spray with flour).
2. Whisk whole-wheat flour, all-purpose flour, baking powder, baking soda, cinnamon, nutmeg and salt in a large bowl.
3. Melt butter in a small saucepan over low heat. Cook, swirling, until it turns a nutty brown, 1 to 3 minutes. Transfer to a bowl to cool.
4. Beat egg whites in a large bowl with an electric mixer on low speed until foamy. Add cream of tartar, increase speed to medium-high and beat until soft peaks form. Gradually add 1/2 cup sugar, beating until stiff but not dry (this can take up to 5 minutes).
5. Combine the melted butter, egg yolk, remaining 1 cup sugar, bananas, oil and vanilla in a large bowl. With mixer on low speed, alternately add the dry ingredients and buttermilk; beat until just blended. Beat in a heaping spoonful of the whites. Using a whisk, fold in the remaining whites. Pour the batter into the prepared pans.
6. Bake the cake until a skewer inserted in the center comes out clean, 30 to 40 minutes. Let cool in the pans on a wire rack for 10 minutes. Invert onto the racks and let cool completely.
7. To prepare frosting and assemble cake: Toast coconut in a pie pan at 350 degrees F until lightly browned and fragrant, 2 to 4 minutes.
8. Combine cream cheese, confectioners' sugar and coconut extract in a large bowl; beat with an electric mixer on medium speed until smooth and creamy.
9. Frost the cake, using a little less than half the frosting between layers and the rest on the top. Garnish with the toasted coconut.

Yield: 12 servings