Chill soufflé dish. Cook ½ cup (1 stick) unsalted butter in a small skillet over medium heat, swirling occasionally, until it foams, then browns, about 4 minutes. Pour into a small heatproof bowl and chill until spreadable, about 20 minutes (butter should be opaque but still soft enough to brush).
Brush bottom and sides of soufflé dish with all of the butter (it will look like a lot), going all the way to the top edges. Sprinkle bottom and sides with ¼ cup (56 g) superfine sugar and tilt dish to coat in an even layer; tap out excess. Chill until ready to use.
Place a rack in middle of oven and preheat to 475°. Place 3.5 oz. bittersweet chocolate (70% cacao), chopped, in a medium heatproof bowl. Heat ½ cup heavy cream in a small saucepan over medium, stirring occasionally, until steaming, about 2 minutes. Pour cream over chocolate and let sit, stirring occasionally with a rubber spatula, until chocolate is melted and mixture is smooth and slightly cooled, about 5 minutes. Add 3 large egg yolks, room temperature, one at a time, whisking until smooth between additions.
Stir ½ cup (50 g) Dutch-process cocoa powder, 1 Tbsp. dark rum (if using), ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, and ½ cup hot water in a measuring glass until combined. Pour cocoa mixture into chocolate mixture and whisk to combine.
Using an electric mixer on medium-high speed, beat 3 large egg whites, room temperature, ¼ tsp. cream of tartar, and ⅓ cup (75 g) superfine sugar in a large bowl until glossy and stiff peaks form, 5–7 minutes.
Gently fold chocolate mixture into egg whites until just combined. Transfer to prepared soufflé dish and evenly sprinkle about 1 Tbsp. superfine sugar over.
Bake soufflé until puffed and top is slightly darkened and just set with a slight wobble in the center when gently shaken, 25–30 minutes.
To serve, dust soufflé with powdered sugar and spoon onto plates. Drizzle with heavy cream.