2¼ cups plus 1 tablespoon cold unsalted butter, cubed
½ cup semisweet chocolate, melted and cooled slightly
Pour the water and sugar into a 1-quart heavy-bottomed saucepan and place over medium-high heat. When the bubbles start to form around the edge of the pan, insert a candy thermometer in the mixture.
Place the egg whites in a large mixing bowl and whip with an electric mixer on medium-high speed until foamy and slightly holding soft peaks. The sugar is ready when it reaches 250 degrees, what is known as the soft-ball stage.
Pour the cooked sugar down the side of the bowl while continuing to whip the egg whites.
Continue whipping the meringue on medium-high speed until the outside of the bowl is warm but not hot, about 5 minutes. Add the butter all at once and beat on medium speed until incorporated. Increase the mixer speed to medium-high and whip until the buttercream is thick, smooth, and shiny, about 10 minutes. At this stage, slowly pour in the chocolate and beat for another 30 seconds or so.
The buttercream can be used immediately or can be stored in the refrigerator for 3 to 4 days or in the freezer for several weeks if kept in an airtight container. If it has been chilled or frozen, allow the buttercream to come to room temperature before using, then whip it with an electric mixer on medium speed until it returns to its initial volume and is once again thick, smooth, and shiny.