Preheat the oven to 350 degrees. Grease a 9-inch springform pan.
In the bowl of an electric mixer, combine the oil and light brown sugar. Beat on medium speed for 3 minutes. Scrape down the sides.
Add the vanilla extract, then add the eggs, one at a time, beating well after each addition. Scrape down the sides.
Combine the flour, spices, baking powder, baking soda and salt together and stir well. Add half of the flour mixture to the mixing bowl. Mix on low speed until just combined. Add the yogurt and mix on low speed until combined. Add the remaining flour mixture and mix until combined.
Add the carrots, coconut, pineapple and walnuts. Fold together with a spatula until the ingredients are evenly distributed.
Pour the batter into your prepared pan. Let sit for 10 minutes before baking.
Bake in a preheated oven for 50-55 minutes until the top springs back when gently poked in the center. The cake should also start to pull away from the sides of the pan when it is done. If the cake is underbaked, it will sink once it cools.
Remove from the oven and cool in the pan for 15 minutes, then remove from the pan and continue to cool on a wire rack.
Frost with cream cheese frosting and serve.