Preheat oven 350 degrees Fahrenheit. Grease bottom and sides of 2 (9 x 1 1/2" or 9 x 2") round layer-cake pans. Dust with flour and shake out excess. Melt chocolate in double boiler over simmering water. Set aside to cool slightly. Drain beet juice into a small bowl. Place beets on a cutting board and chop into very small pieces. Add to beet juice and set aside.
Beat butter, sugar, eggs and vanilla in a large bowl with an electric mixer on high speed until very fluffy, about 5 minutes, scraping sides occasionally. Reduce speed to low and beat in melted chocolate.
Stir together flour, baking soda and salt in a medium-size bowl. With mixer on low speed, alternately beat flour in fourths and buttermilk in thirds into chocolate mixture, beginning and ending with flour. Mix until incorporated, about 1 minute. Add beets and juice and mix on medium speed until blended, about 1 minute. The batter will be thin and you will see pieces of beets.
Divide the batter equally between the 2 prepared pans. Bake in the 350 degrees oven for 30 - 35 minutes or until cake tester inserted in center comes out clean and top of cake springs back when lightly pressed with fingertips. DO NOT over bake or cake will be dry. Cool cakes in pans on wire racks for 10 minutes and then invert onto racks.
NOTE: If desired, cake layers may be wrapped in foil and kept at room temperature overnight, or they may be frozen. Defrost wrapped cake at room temperature before frosting.
Heat cream in a medium-size saucepan just until it comes to a boil. Remove from heat and add chocolate and vanilla, stirring until mixture is smooth and chocolate is melted. Transfer mixture into a plastic or glass bowl (metal causes the sides to get too cold and set up too quickly.) Refrigerate, stirring every 10 minutes until mixture is as thick as pudding, about 50 - 60 minutes. At this point the frosting will begin to set up very quickly. Leave in refrigerator and stir every 5 minutes until frosting is a thick as fudge, about 15 more minutes. Alternatively, the frosting may be placed over ice water and stirred constantly until spreading consistency. If it begins to get too thick, immediately remove it from the water.
To assemble the cake, (make sure cake has cooled and has reached room temperature) place one cake layer top-side down on serving platter. Spread with a third of the frosting and top with second layer, bottom-side up. Spread remaining frosting over top and sides. Let stand at room temperature for frosting to set.
NOTE: The frosted cake may be held at room temperature, uncovered, overnight or refrigerated up to 2 days. Bring to room temperature before serving.