Preheat your oven to 350°F (175°C). Prepare and grease a 1 lb. loaf pan. Add flour if your pan is prone to sticking. (you could also line your pan with parchment paper) If you're using a smaller loaf pan than 1 lb. , you most likely will have to divide your batter between two loaves.
In a large mixing bowl, beat together the 4 eggs, 1 1/4 cups brown sugar, and 3/4 cup sugar for 4 minutes until well combined and slightly fluffy.
Add 1/2 cup vegetable oil, 1 tablespoon vanilla extract, and 1/2 cup sour cream to the egg and sugar mixture. Mix for 30 seconds to 1 minute until fully incorporated.
In the same bowl, add 2 1/4 cups all-purpose flour, 3/4 teaspoon salt, 2 teaspoons baking soda, 2 teaspoons baking powder, 1 tablespoon cinnamon, and 1/4 teaspoon nutmeg. Mix the dry ingredients into the wet ingredients just until incorporated, about 30 seconds.
Avoid over-mixing, as it can affect the final texture of the carrot cake.
Fold in 3/4 cup coconut shreds, 1 cup roughly chopped walnuts, and 3 cups shredded carrots using a rubber spatula. Mix until all the ingredients are well incorporated.
Pour the batter into the prepared loaf pan and smooth the top with the spatula.
Bake in the preheated oven for about 55-60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for about 10 minutes. Then transfer it to a wire rack to cool completely.
Once the cake is completely cooled, you can frost it with your choice of frosting, such as cream cheese frosting or buttercream frosting. We're making cream cheese frosting today!