Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger until well combined.
In a large bowl, beat the granulated sugar, brown sugar, and vegetable oil until smooth.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots, shredded coconut, and chopped walnuts.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
While the cake cools, prepare the cream cheese frosting: In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.
Gradually add the powdered sugar, beating until combined.
Add the vanilla extract and milk, and beat until the frosting is smooth and spreadable.
Once the cake is completely cool, spread the cream cheese frosting evenly over the top.
Slice and serve.