Preheat the oven to 350 degrees F. Lightly spray a 10-inch springform pan with nonstick spray.
In a medium bowl, stir together the all-purpose flour, whole wheat flour, baking soda, cinnamon, nutmeg, and salt. Set aside.
In the bowl of a standing mixer fitted with the paddle attachment or a large mixing bowl, beat together the egg, egg whites, brown sugar, canola oil, and vanilla extract on medium speed until well combined. Add the grated carrots and beat for 1 minute. Add the pineapple and shredded coconut and beat just until incorporated.
With a wooden spoon, stir in half of the flour mixture, just until the flour almost disappears. Stir in the buttermilk. Add the remaining flour mixture, continuing to stir in by hand, just until combined. Gently fold in the walnuts and raisins.
Pour the batter into the prepared baking pan. Bake for 40 to 45 minutes, until a toothpick inserted into the center comes out clean. (Check at the 30-minute mark—if the edges of the cake are browning too quickly, tent with foil, then return to the oven to finish baking.) Remove the cake from the oven and let cool completely in the pan. Run a dull knife, such as a butter knife, along the edge of the cake to loosen, then unmold it. Carefully transfer the cake to a serving plate.
Meanwhile, prepare the frosting: In a medium bowl, beat together the cream cheese, Greek yogurt, butter, vanilla extract, almond extract (if using), and salt at medium speed for 2 minutes, until fluffy and well combined. Reduce the mixer speed to low and gradually add the powdered sugar, increasing the speed to medium as you go. Beat for 1 to 2 minutes until well combined.
Spread the frosting evenly over top of the cooled cake. Sprinkle with toasted nuts and serve.
TO STORE: This cake may be stored in the refrigerator, covered, for up to 1 week. Let come to almost room temperature before serving.
TO FREEZE: Wrap and freeze individual slices of this cake in an airtight freezer-safe storage container for up to 3 months. Remove and thaw in the refrigerator as desired. You can also freeze the entire cake.