Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 8" round pans.
In a mixer or large bowl, beat together eggs, oil, sugar and vanilla. In a separate bowl sift together the flour, baking soda, baking powder, salt, nutmeg and cinnamon. Add the flour mixture into the wet ingredients and mix to combine. Stir in carrots. Fold in toasted pecans. Pour into prepared pans.
Bake in the preheated oven for 35 to 40 minutes for 2 8" round pans, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.
To Make Frosting: Combine butter, cream cheese, confectioners' sugar and 1 teaspoon vanilla. Beat until the mixture is smooth and creamy. Frost the cooled cake.