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Set a saucepan with about 1” of water in it over high heat. Bring the water to a boil then reduce the heat so that the water is just barely simmering.
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As the water is heating, combine the chocolate with the butter in a large metal bowl or the bowl of a stand mixer. Set the bowl over the saucepan, ensuring the bottom isn’t touching the water.
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Heat the chocolate and butter, stirring regularly, until both have melted. Stir until smooth.
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Remove the bowl from the heat and stir in the vanilla and salt.
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Sift the confectioners’ sugar with the cocoa powder and add about half to the chocolate-butter mixture.
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Using the lowest speed on your hand or stand mixer, mix until thoroughly combined; the frosting will be quite stiff. Stir in the sour cream; the frosting will look lumpy. Increase the speed to medium and mix until smooth, 30 to 60 seconds.
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Add the remaining confectioners’ sugar and cocoa powder mixture, mixing slowly at first. Once everything is thoroughly combined, increase the speed to medium-high and beat the frosting until it’s light and fluffy, about 2 minutes.
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Use the frosting immediately; it’ll firm up as it sits, almost like soft fudge.
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If you are not planning to use the frosting right away, cover the bowl and refrigerate until needed. When you are ready to use the frosting, let it sit for an hour or so at room temperature before beating it until it’s soft and spreadable.