For the carrot cake: Preheat the oven to 350 degrees F. Grease the bottom of a 13-by-9-by-2-inch baking pan with cooking spray, line with parchment paper and grease the paper with cooking spray.
With an electric mixer, cream the granulated sugar, oil, vanilla and eggs together in a large bowl. Sift together the flour, baking soda, cinnamon and salt in a separate bowl. Add the dry ingredients to the sugar mixture and mix well. Add the carrot puree, coconut, walnuts and pineapple and beat until smooth.
Pour the batter into the prepared pan and bake until a toothpick inserted into the center comes out clean, 40 to 45 minutes. Cool the cake for about 5 minutes. Spray a wire rack with cooking spray. Run a knife around the edges of the pan and turn the cake out onto the wire rack. Cool completely before frosting.
For the frosting: Using an electric mixer, beat the Neufchatel in a medium bowl until smooth. Slowly add the confectioners' sugar and continue beating until fully combined. Mix in the vanilla.
Frost the cake and garnish with the chopped walnuts. Refrigerate until ready to serve.