Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, ground nutmeg, and ground ginger until well combined.
In a large bowl, beat the granulated sugar, light brown sugar, and vegetable oil until smooth.
Add the eggs one at a time to the sugar and oil mixture, beating well after each addition.
Stir in 2 teaspoons vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots, shredded sweetened coconut, and chopped walnuts until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 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 is cooling, prepare the frosting. In a medium bowl, beat the softened cream cheese and unsalted butter until smooth and creamy.
Add the powdered sugar gradually, beating until the frosting is smooth and fluffy.
Stir in 1 teaspoon vanilla extract.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.
Cut into 12 squares and serve.