Preheat the oven to 350°F (175°C) and grease the bottom of an 8-inch cake pan.
Using a grater, finely shred the carrots and measure out 2 cups.
2 cups grated carrots
In a large mixing bowl, whisk together eggs, sugar, ground cinnamon, ground nutmeg, and vegetable oil until the mixture is smooth and slightly thickened, about 2-3 minutes. Watch for the mixture to become glossy and uniform.
2 cups grated carrots
Add the grated carrots to the wet mixture and fold gently until evenly combined.
2 cups grated carrots
In a separate bowl, sift together flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, folding until just incorporated. The batter should be thick but pourable.
2 cups grated carrots
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Bake in the preheated oven until the surface is golden brown and a toothpick inserted into the center comes out clean, approximately 40 minutes. Watch for the edges to pull slightly away from the pan and for a pleasant aroma to develop.