Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan and set aside.
In a large mixing bowl, combine sifted flour, sugar, ground cinnamon, nutmeg, baking powder, and salt. Whisk together until evenly distributed.
In a separate bowl, beat the eggs, then add vegetable oil and vanilla extract. Mix until the mixture is smooth and slightly frothy.
Pour the wet mixture into the dry ingredients and stir gently until just combined. Fold in the grated carrots until evenly incorporated. The batter should be thick but spreadable.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Place in the oven and bake for 40 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then, transfer to a wire rack to cool completely before frosting or serving.