Preheat oven to 350 degrees Fahrenheit. Grease a 9-inch skillet with flour and brush with flour.
In a large bowl, combine grated carrots, flour, white sugar, baking soda, baking powder, salt, and cinnamon. Add eggs, oil, 1 teaspoon of vanilla, pineapple, and 3/4 cup chopped pecans, stirring. Pour the mixture into a prepared pan.
Bake in the preheated oven for 30 to 40 minutes, or until a toothpick comes out clean in the center of the cake. Let it cool down.
To make frosting:
In a medium bowl, combine confectioners’ sugar, Neofchatel cheese, 1/2 cup of butter or margarine, and 1 1/4 teaspoon of vanilla. Whisk until smooth, then stir in 1 cup chopped pecans. Spread on a chilled cake.