Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 (9 inch) pans. In the top of a double boiler, heat chocolate, stirring occasionally, until chocolate is melted and smooth. Remove from heat and allow to cool to lukewarm. Sift together the flour, sugar, baking soda and salt. Set aside.
In a large bowl, beat shortening until smooth. Add flour mixture, 1 cup of the milk and vanilla. Mix on low speed until flour is dampened, then beat on medium speed for 2 minutes. Add eggs, remaining 1/3 cup milk and melted chocolate. Beat on medium speed for 1 minute. Pour batter into prepared pans.
Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.