Prepare two 12-well cupcake pans by inserting a paper cupcake liner into each well.
Melt the unsweetened baking chocolate and unsalted butter in the top of a double boiler.
Set aside and allow to cool somewhat while you mix the remaining ingredients.
In a large bowl, combine the flour, white and brown sugars, salt, baking soda, and baking powder.
In another bowl, dissolve the coffee powder in the hot water.
Add the sour cream, eggs, and vanilla.
Pour the liquid ingredients into the dry ingredients and mix well.
Pour the melted chocolate and butter into the batter and mix well.
Divide the batter evenly between the wells in each of the cupcake pans (about 1/4 cup batter works well).
Bake 25 to 35 minutes or until fork inserted into middle of one of the cupcakes comes out clean.
Remove cupcakes to cooling racks and cool completely before frosting.
To make the frosting: Place the white chocolate in a small microwave-safe bowl. Microwave on medium (50% power) for 1 minute. Stir. Microwave 30 seconds more or until chocolate is softened. Stir until smooth and let cool.
Beat cream cheese in bowl until light and fluffy, using electric mixer at medium speed. Beat in butter, vanilla and salt. Gradually beat in cooled chocolate until smooth. Add the confectioners and brown sugars and beat about 2-3 minutes. Stir in chopped pecans and coconut; fold until incorporated.