Melt the chocolate first: Place the chopped dark chocolate in a heatproof bowl set over barely simmering water (bowl should not touch the water). Stir until smooth, then remove from heat. Whisk in the vanilla bean paste and espresso powder. Let the mixture cool to about 80–85°F (it should be fluid but not warm).
Degrease your mixer bowl and whisk with a little vinegar or lemon juice and wipe dry. Add the egg whites, sugar, and salt to the bowl and whisk to combine thoroughly.
Set the bowl over a pot of gently simmering water, ensuring the bottom of the bowl doesn’t touch the water. Heat, whisking steadily, until the mixture reaches 150–155°F and feels completely smooth when rubbed between two fingers (no sugar grit). This usually takes 5–7 minutes.
Move the bowl to the stand mixer fitted with the whisk. Whip on medium speed for 5–7 minutes, then increase to medium-high and beat until the meringue is glossy, thick, and the bowl is cool to the touch, 3–5 minutes more. Drop to low for 30 seconds to even out the texture.
Switch to the paddle attachment. With the mixer on medium-low, add the butter two tablespoons at a time, letting each addition incorporate before adding the next. Scrape the bowl once or twice. If the mixture looks curdled or thin, keep mixing; if it stays soupy, chill the bowl for 10 minutes and beat again until smooth.
With the mixer on low, add the cooled chocolate mixture in two additions. Increase to medium-high and beat until the buttercream is uniformly chocolaty and satiny, about 2 minutes.
Finish by running the mixer on the lowest speed for 30–60 seconds to gently deflate any large air bubbles. Use immediately, or see storage notes.
Practical tip: If the buttercream ever seems slightly broken after adding chocolate, briefly warm the outside of the bowl with your hands or a warm towel for 10–15 seconds, then mix on medium until it comes together.