Beat egg.
In a saucepan, combine egg, unsweetened chocolate squares,1 cup sugar, and milk.
Heat slowly, stirring frequently, until the chocolate melts and the mixture thickens.
Remove from heat, set aside, allowing to cool to room temperature.
In a large bowl, mix 1/4 cup butter and 1/2 cup shortening.
Add 1 1/2 cups sugar and cream together.
Add vanilla and eggs, beating and mixing well.
In a separate bowl, mix together flour, baking soda, and salt.
Alternately add in flour mixture and milk, beating until smooth.
Blend in chocolate mixture.
Grease 3- 9 inch round cake pans.
Pour batter into cake pans.
Bake in a preheated oven at 350° F for 25 – 30 minutes.
Test for doneness with a toothpick.
Remove from oven and place on wire racks to cool.