Preheat the oven to 350°F (175°C). Grease and flour a baking pan.

In a mixing bowl, whisk together the flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.

In another bowl, beat the eggs and mix in the vegetable oil.

Add the grated carrots to the wet mixture and stir until combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Pour the batter into the prepared baking pan and smooth the top.

Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.

Allow the cake to cool completely before frosting.

In a mixing bowl, beat the softened cream cheese and butter until smooth.

Gradually add the powdered sugar and vanilla extract, mixing until creamy.

Spread the frosting evenly over the cooled cake.