Cut up the butter and place it with the chocolate in a heatproof bowl set over simmering water. Cook, stirring if needed, until the ½ cup unsalted butter and 3 ounces semisweet chocolate are fully melted.
Remove from the heat and stir until very smooth, then use to frost your favorite cake or cupcakes! The icing will firm up a bit as it cools.
Notes
Make sure the chocolate is all melted. This is a luxuriously smooth icing so you NEED to ensure that the chocolate it totally melted! If you pull the bowl off the heat and notice there are some lumps of unmelted chocolate, return it to the stove and heat it a little longer so that it's completely smooth.
Cool it a bit. The icing will be quite warm to hot when you take it off the stove. I like to let it cool for about 10 minutes before icing my cake.
Add to a cooled cake. In that same vein, you'll want to make sure your cake is completely cooled before adding the icing. If the cake is warm, it may melt the icing.
It will firm as it cools. If the icing seems a bit goopy or liquidy when you add it to the cake, don't worry! It will firm and set up as it cools.