Preheat the oven to 350°F.
Grease and flour two 9-by-3-inch cake pan.
Mix the flour, sugar, baking powder, baking soda, cinnamon and nutmeg in a mixing bowl and set aside.
In another bowl, with a fork, mix the eggs, oil and carrots.
Add the dry ingredients and mix well.
Divide the batter into the previously prepared cake pans and bake 30-35 minutes, until a toothpick inserted into the center of the cakes comes out clean.
Transfer the pans to two wire racks and let them cool for 10 minutes.
Unmold the cakes and let them completely cool down before frosting.
Put the pecans in a shallow baking pan, and bake them for 8 to 10 minutes, until fragrant.
Chop the pecans and save some halves for decoration purposes.
In a bowl, soften the cream cheese by microwaving it for 45 seconds to 1 minute.
Add the butter and vanilla extract and beat them with an electric mixer until light and fluffy.
Gradually add the sugar, beating well until it gets the desired consistency.
Frost the top of one cake with cream cheese frosting and sprinkle with the chopped pecans.
Put the other cake on top. Frost sides and top. Put some pecans halves on top.
Refrigerate at least one hour before serving.