Preheat oven to 325F/160C. Grease an 8-inch/20cm square pan and line the base and sides of the pan with parchment paper.
Place chocolate, butter, milk, and sugar in a bowl and set the bowl over a saucepan of simmering water, making sure the water doesn’t touch the bowl, and stir occasionally. Remove from heat when chocolate and butter have melted, and stir mixture until completely smooth. Allow mixture to cool at room temperature for 15 minutes.
Add vanilla and eggs to chocolate mixture and stir until well combined.
In a large bowl mix together flour, baking powder, and salt. Add one cup of chocolate mixture to the flour and stir until a smooth paste forms. Repeat with another cup of the chocolate mixture. Add remaining chocolate mixture and stir until mixture is smooth. This gradual method of combining the wet and dry ingredients helps to prevent lumps. Pour mixture into prepared pan.
Bake for 45 to 60 minutes, until a toothpick inserted into the center of the cake comes out clean without any batter. If the cake is browning too much while baking, cover it loosely with aluminum foil. Allow cake to cool on a wire rack to room temperature.
To make the ganache: Place white chocolate in a bowl and set the bowl over a saucepan of simmering water, making sure the water doesn’t touch the bowl, and stir occasionally. When chocolate has completely melted, remove from heat and quickly stir in sour cream. Use immediately to frost cake, or if the ganache is quite runny, set it aside at room temperature to thicken slightly before using.
Store cake in an airtight container in the refrigerator. Bring to room temperature before serving. The cake is suitable to freeze with or without icing.