Set up a double boiler: Fill a medium pot with 1–2 inches of water and bring to a gentle simmer over medium heat. Place a heatproof mixing bowl (glass or stainless steel) on top, making sure the bottom of the bowl does not touch the water.
Warm the egg whites & sugar: Add 2 egg whites and ⅔ cup dark brown sugar to the mixing bowl. Whisk often, making sure to scrape down any brown sugar that creeps up the sides. Cook gently over low heat until mixture reaches 160° F on an instant-read thermometer and sugar has fully dissolved (rub a little between your fingers — there should be no gritty sugar crystals).
Whip and cool: Remove bowl from heat and transfer to a stand mixer fitted with the whisk attachment. Whip on medium-high speed until the meringue becomes glossy, voluminous, and the mixture has cooled to about 90°F, 3-5 minutes. The bowl should feel just slightly warm to the touch.
Add butter: With mixer on medium speed, add softened butter 1 tablespoon at a time, allowing each addition to incorporate before adding the next. The mixture may look curdled at first, but keep mixing! It will smooth into a silky buttercream eventually.
Finish with vanilla: Add 2 tsp vanilla; beat on medium speed for 1–2 more minutes, until the buttercream is smooth, fluffy, and completely emulsified.