Hi Michelle:-) The following is the recipe from The New Basics Cookbook. I think it is the recipe that you are looking for.

BERTA'S CARROT CAKE
Source: The New Basics Cookbook by Julee Rosso, Sheila Lukins
Yield: 12 portions

"Carrot Cakes abound, but there's none better than the one created by Sheila's mother. It has just the right texture and taste - and not too sweet. Try it unfrosted for breakfast. It's a classic for us and it will be for you."

2 cups unbleached all-purpose flour
2 cups granulated sugar
2 tsp. baking soda
2 tsp. ground cinnamon
1 cup corn oil
3 eggs, lightly beaten
2 tsp. vanilla extract
1 1/3 cups pureed, cooked carrots
1 cup chopped walnuts
1 cup shredded coconut
3/4 cup canned crushed pineapple, drained
Cream Cheese Frosting (recipe follows)
Confectioner's sugar for dusting

Preheat the oven to 350 degrees F. Line a 13 X 9-inch layer cake pan with waxed paper, and grease the paper.

Sift the flour, sugar, baking soda, and cinnamon together in a large bowl. Add the oil, eggs, and vanilla, and beat well. Then fold in the carrots, walnuts, coconut, and pineapple. Pour the batter into the prepared pan.

Place it on the middle rack of the oven and bake until the edges have pulled away from the sides of the pan and a toothpick inserted in the center comes out clean, 1 hour.

Cool the cake in the pan for 10 minutes. Then invert it over a cake rack and unmold, remove the waxed paper, and continue to cool for 1 hour.

Frost the top and sides of the cooled cake with cream cheese frosting, and dust the top with confectioner's sugar.

CREAM CHEESE FROSTING
Frosting for a 13 X 9-inch cake.

4 oz. cream cheese, at room temperature
3 tablespoons unsalted butter, at room temperature
1 1/2 cups confectioner's sugar
1/2 tsp. vanilla extract
Juice of 1/4 lemon

Cream the cream cheese and butter together in a mixing bowl.

Slowly sift in the confectioner's sugar, and continue beating until fully incorporated (there should be no lumps). Stir in the vanilla and lemon juice.