Preheat oven to 350°F. Spray a 9x13 baking pan with non-stick cooking spray and set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.
In a separate large mixing bowl, whisk together the oil, eggs, brown sugar, granulated sugar, crushed pineapple, and vanilla extract until fully combined. Add the grated carrots and chopped walnuts to the wet ingredients and stir until well combined.
Add the dry ingredients to the wet ingredients and mix with a whisk or rubber spatula until just combined, making sure not to over mix the batter.
Pour the cake batter into the prepared baking pan and spread around into one even layer. Bake at 350°F for 35-45 minutes or until the top of the cake is set and a toothpick inserted into the center of the cake comes out clean. If needed, tent with foil for the last 15-20 minutes of baking to prevent excess browning on top of the cake.
Remove from the oven, transfer to a wire rack, and allow to cool completely in the pan.