Preheat oven to 350 degrees F. Combine flour, baking powder, baking soda, cinnamon and nutmeg in a bowl. Set the flour mixture aside.
Using an electric mixer, beat the eggs, canola oil, vanilla extract and sugar until smooth, about 20 seconds. Add the flour mixture and mix well. Fold in grated carrots and walnuts.
Spoon batter into a 8x11-inch baking pan (or baking dish) coated with cooking spray. Bake on the middle rack of the oven until toothpick or skewer inserted into center of cake comes out clean, about 50-60 minutes.
Remove from oven and let it cool in the pan for 10 minutes. Then run a thin-bladed knife around the edges to loosen.