1. Using a hand mixer, beat the butter until smooth and creamy, starting on low speed to break up the clumps, then on medium for about 4 minutes. Stop and scrape down the paddle, bottom, and sides of the bowl. Add the vanilla and beat for another minute.
2. On low speed, add the sugar, mixing until combined. Stop and scrape down the bottom and sides of the bowl.
3. Carefully pour the melted chocolate into the bowl, being careful not to let it touch the sides of the bowl or the paddle. If the butter is colder than the chocolate, the chocolate will seize up when it touches the cold bowl. Mix on low speed until all the chocolate has been added. Scrape down the bottom and sides of the bowl.
4. Once fully combined, turn the mixer to medium speed and mix for about 4 minutes. Scrape down the bottom and sides of the bowl. Mix again on low speed until you no longer see streaks of butter, 1 or 2 minutes.
5. Remove the mixer from the bowl and scrape the bottom and sides of the bowl with a spatula.
6. Return to the mixer on medium speed for about 10 seconds, just to incorporate any of the butter bits from the bottom. If you mix too much, the icing will be too light. Add the tablespoon of cream or milk if you need to adjust the consistency of the buttercream for it to spread easier.
7. Store the icing at room temperature in an airtight container for up to 3 days.

Makes: 5 cups (enough for one 9-inch or 24 cupcakes)