Begin by preheating your oven to 350°F (175°C). Grease a 9x13-inch baking pan or line it with parchment paper for easier removal and clean-up.

In a medium bowl, sift together the all-purpose flour, baking soda, and salt. Set this mixture aside for later use.

In a large mixing bowl, beat the butter and brown sugar together until the mixture becomes light and fluffy. Incorporate the eggs one at a time, ensuring each is fully blended before adding the next. Stir in the vanilla extract followed by the melted unsweetened chocolate.

Add half of the sifted dry ingredients to the creamed mixture, followed by half of the sour cream. Mix gently until combined. Repeat with the remaining flour mixture and sour cream until everything is incorporated evenly.

Gradually pour the boiling water into the batter, stirring continuously until smooth. The batter will appear thin, which is expected and essential for the cake’s moist texture.

Pour the batter into the prepared baking pan and spread evenly. Bake in the preheated oven for approximately 35 minutes, or until a toothpick inserted into the center comes out clean. Once baked, remove the cake from the oven and allow it to cool in the pan for about 10 minutes before icing.

While the cake cools slightly, melt the butter in a saucepan over medium heat. Stir in the brown sugar and allow it to boil gently for approximately 2 minutes. Add the milk and bring the mixture to a boil once more. Remove the pan from heat and place it in cold water. Stir in the confectioners' sugar and whisk until smooth and spreadable.

Spread the warm caramel icing evenly over the still-warm cake. Allow the cake to cool completely before slicing and serving.