In the bowl of an electric mixer, beat the cream cheese on medium speed with the sour cream until it's creamy. Add the salt.
Add about a third of the sugar to the cream cheese, then half the milk. Mix till smooth, then add another third of the sugar and the rest of the milk. Mix till smooth again, then add the rest of the sugar and again blend till smooth.
While the mixing is going on, melt the chocolate in the microwave in a glass measuring cup. Microwave for a minute on about 70 percent power, then stir--even if the chocolate doesn't look melted at all. Continue to microwave in 15-second bursts, stirring between each, until the chocolate is completely melted and smooth.
Add the chocolate a tablespoon at a time to the frosting mixture while the beater is running. After all the chocolate has been added, scrape down the sides of the bowl with a rubber spatula, and mix until completely smooth.