Chop the chocolates and place them in a heat-proof bowl set over a pan simmering water. Stir until melted and set aside until cooled to room temperature.

Mix the egg whites, sugar, cream of tartar, and salt in the bowl of an electric mixer fitted with a whisk attachment. Place the bowl of egg whites over the pan of simmering water and heat the egg whites until they are warm to the touch, about 5 minutes. Return the bowl to the electric mixer and whisk on high speed for 5 minutes, or until the meringue is cool and holds a stiff peak.

Add the butter, 1 tablespoon at a time, while beating on medium speed. Scrape down the bowl, add the melted chocolate, vanilla, espresso, and rum, if using, and mix for 1 minute or until the chocolate is completely blended in. If the buttercream seems very soft, allow it to cool, and beat it again.