Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch pan.

Combine grated carrots, flour, white sugar, baking soda, baking powder, salt, and cinnamon in a large bowl; stir in eggs, oil, 1 1/4 teaspoons vanilla, pineapple, and 3/4 cup chopped pecans. Spoon batter into prepared pan.

Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 30 to 40 minutes. Let cake cool.

To make the frosting: Combine confectioners' sugar, Neufchatel cheese, 1/2 cup butter and 1 1/4 teaspoons vanilla in a medium bowl; beat until smooth. Fold in 1 cup chopped pecans. Spread frosting on cooled cake.