Preheat oven to 350 degrees. Grease and flour a 9X13 pan. In a large bowl, beat together eggs, oil, white sugar, and 2 teaspoons of vanilla. Mix in flour and baking soda, baking powder, salt, and cinnamon.
Stir in carrots. Fold in pecans. Pour into prepared pan.
Bake in the preheated oven for 40-50 minutes oruntil 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.
For frosting: In a medium bowl, combine butter, confectioners sugar, and 1 teaspoon of vanilla. Beat until the mixture is smooth and creamy. Stire in chopped pecans. Frost the cooled cake.
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