Prepare the cake mix according to package directions and bake in a greased 9- inch round springform pan. Note: Set the pan on a baking sheet to catch any drips. Set aside and let cool completely.
If using a standard size box of cake mix (something other than Jiffy), follow the directions for two 9-inch layers, but bake one layer in the springform pan and bake the other in 9-inch cake pan. Freeze the other layer and use it for something else. Alternatively, weigh out half the box and half the add-in ingredients.
In a large mixing bowl, beat the cream cheese, vanilla and sugar until well blended. Reduce speed to low and add the sour cream, then stir in the eggs (still using low speed and being careful not to overbeat). Pour this mixture over the baked and cooled cake.
Bake for 35 minutes. Let cake cool completely, then loosen from rim and remove made rim. Note: after 35 minutes, cake should still be kind of jiggly in the center. It will firm as it cools and chills.
When cake is completely cool, prepare the icing. Measure out all your ingredients and have them ready to go, and have the 2 tablespoons of water in a microwave-safe measuring cup. Make sure you sift the powdered sugar.
In a medium saucepan, melt the butter over medium heat. Reduce heat to low and add the chopped chocolate. Stir until smooth. Meanwhile, heat the water in the microwave-safe cup until boiling. Remove chocolate mixture from heat and add boiling water and powdered sugar. Stir well, then add the vanilla and stir until smooth. Pour over the top of the cake and chill for several hours.