I hope it is similar to the one from Starbuck's that you are looking for. It is delicious:-)!!

ITALIAN CREAM CAKE
Source: The Cotton Country Collection Cookbook by The Junior Charity League of Monroe, Louisiana

CAKE:
2 cups sugar
1/2 cup canola oil
1 stick (1/2 cup) butter
5 eggs, separated
1 cup buttermilk
1 tsp. baking soda
2 cups flour
1 cup shredded coconut
1/2 cup nuts, chopped (I use pecans)
1 tsp. vanilla
ICING:
1 (8 oz.) package cream cheese, softened
1 stick (1/2 cup) butter, softened
1 box powdered sugar
1/2 cup nuts (pecans), chopped fine
1 tsp. vanilla

CAKE:
Cream sugar, oil, and butter. Add egg yolks, one at a time, beating after each addition.

Stir baking soda into buttermilk.

Add sifted flour into batter, alternating with buttermilk mixture. Add coconut chopped nuts, and vanilla.

Beat egg whites and fold into mixture. Pour into a greased and floured 9x13 inch cake pan or three 8 or 9 inch layer cake pans.

Bake at 325 degrees F for 45 minutes. Cool and ice.

ICING:
Beat cream cheese and butter. Add powdered sugar, nuts, and vanilla. Continue to beat until of spreading consistency.