First, beat the egg.
Then, in a saucepan, combine the 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 the flour, baking soda, and salt.
Alternately, add in the flour mixture and milk, beating until smooth.
Blend in the chocolate mixture.
Grease three 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 the cake from the oven and place it on wire racks to cool.