Yummy Chocolate Cream Cheese Cake

1/2 cup butter
1/2 cup vegetable oil
1 1/4 cups white sugar
2 eggs
2 cups grated zucchini
1/2 cup buttermilk
2 1/2 cups all-purpose flour
1/4 cup unsweetened cocoa powder
1 teaspoon baking powder
1 teaspoon salt

Fillling:
1 (8 ounce) package cream cheese, softened
2 tablespoons butter, softened
1/4 cup white sugar
1 tablespoon cornstarch
1 egg
2 tablespoons milk
1/2 teaspoon vanilla extract

Directions:
1. Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan. Sift together the flour, cocoa, baking powder and salt. Set aside.
2. In a large bowl, cream together 1/2 cup butter, oil, and 1 1/4 sugar until light and fluffy. Beat in 2 eggs, one at a time, then stir in the zucchini. Beat in the flour mixture alternately with the buttermilk. Pour half of the batter into prepared pan.
3. Make the filling: In a medium bowl, beat cream cheese, 2 tablespoons butter. Combine 1/4 cup sugar and cornstarch; beat into the cream cheese mixture until smooth. Beat in 1 egg, milk and vanilla. Pour over batter in pan, distributing evenly. Pour remaining batter over filing.
4. Bake in the preheated oven for 50 to 60 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.