Preheat oven to 350. In a large bowl, beat 4 eggs, 1 1/4 cups vegetable oil, 2 cups white sugar, and 2 teaspoons vanilla. Mix in 2 cups all-purpose flour, 2 teaspoons baking soda, 2 teaspoons baking powder, 1/2 teaspoon salt, and 2 teaspoons ground cinnamon. Stir in 3 cups grated carrots. Fold in 1 cup chopped pecans. Pour into greased and floured 9x13 inch pan. Bake 40 to 50 minutes, until a toothpick inserted into center comes out clean. Cool in pan for 10 minutes, then turn onto a wire rack and cool completely.

Frosting: In a medium bowl, combine 1/2 cup softened butter, 8 ounces softened cream cheese, 4 cups 10x powdered confectioners' sugar, and 1 teaspoon vanilla. Beat until smooth and creamy. Stir in 1 cup chopped pecans. Frost the cooled cake.