Pre-heat oven to 350F degrees.
In a large bowl, cream the butter at high speed for one minute. Add the brown sugar, baking soda and salt and continue to mix until they are well combined. Beat in the egg and vanilla. Now beat in the melted chocolate, then the sour cream.
Begin to mix in the flour in thirds until well combined and the dough begins to stiffen. You may need to add the last bit by hand using a wooden spoon.
Chill dough for 30 minutes.
Place rounded teaspoons of dough on an untreated baking sheet about two inched apart . Bake for 8 to 10 minutes, until the edges are firm.
Remove cookies to a cooling rack to cool. Once cool, spread a small amount of frosting on each cookie (frosting directions appear below). These will keep in a tightly covered container for three days. You can also freeze the cookies before frosting for up to one month.
To prepare the frosting, place the butter, salt and vanilla in a medium bowl and whip until light and fluffy. Gradually beat in the cocoa and one cup of the powdered sugar. Add in the milk to soften the frosting a bit. Add in the remaining powdered sugar in parts, mixing well until incorporated. If it get too thick for spreading, then add a bit more milk.