Preheat oven to 350 degrees F (175 degrees C). Lightly grease and flour a 9x13-inch cake pan or two 8-inch round cake pans.
Place cake mix in a large mixing bowl. Add eggs, milk, and vanilla extract and beat with an electric mixer on low speed for 1 minute. Increase speed to medium-high and beat for 2 more minutes, scraping sides of bowl as needed. Transfer batter to cake pan.
Bake in preheated oven until a toothpick inserted into center of cake comes out clean; 40 to 50 minutes for a 9x13-inch cake pan, or 25 to 35 minutes for 8-inch cake pans. Allow cake to cool for 10 minutes.
Crumble cake while warm into a large bowl. Stir in frosting until well blended.
Melt chopped chocolate and shortening in a glass bowl in the microwave, on medium heat, until melted, about 1 minute. Alternatively, melt chopped chocolate and shortening in a metal bowl over a pan of simmering water, stirring occasionally until smooth.
Form balls of the chocolate cake mixture using a melon baller or small scoop. Dip balls in warm chocolate mixture, using a toothpick or fork to hold them. Place on waxed paper to cool.