Preheat the oven to 350°F (175°C). Grease an 8-inch cake pan and line the bottom with parchment if preferred.

Peel and grate the carrots finely until you have 2 packed cups. Set aside.

In a large bowl, crack in the eggs and add the sugar, cinnamon, nutmeg, and oil. Whisk vigorously for 2 to 3 minutes until the mixture looks glossy and has thickened slightly.

Fold the grated carrots into the wet mixture until evenly distributed.

In a separate bowl, sift together the flour, baking powder, and salt.

Add the dry ingredients to the wet mixture in two additions. Fold gently with a spatula just until there are no streaks of flour. Avoid overmixing to keep the cake tender.

Pour the batter into the prepared pan and smooth the top with the back of a spoon or an offset spatula.

Bake for about 40 minutes. A toothpick inserted in the center should come out clean or with a few moist crumbs.

Let the cake cool in the pan for 10 minutes, then turn out onto a rack to cool completely before slicing.