Preheat oven to 375 degrees. Place four 6- to 8-ounce ovenproof bowls on a rimmed baking sheet.

Place chocolate and butter in a heatproof bowl set over (not in) a saucepan of gently simmering water. Stir occasionally just until melted, 4 to 5 minutes. Remove from heat; mix in 2 tablespoons sugar, then egg yolks and vanilla.

In a medium bowl, with an electric mixer, beat egg whites and salt until soft peaks form. With mixer running, gradually add remaining 2 tablespoons sugar; beat until mixture is stiff and glossy.

Using a flexible spatula, fold about a third of egg-white mixture into chocolate mixture; gently fold in remaining egg-white mixture just until combined. Divide among bowls. (Puddings can be prepared in advance up to this point; cover with plastic wrap and refrigerate up to 1 day.)

Bake until tops are puffed and cracked but insides are still quite soft (a toothpick inserted in center will come out gooey), 20 to 25 minutes (or 25 to 30 minutes if refrigerated). Serve warm or at room temperature (puddings will sink as they cool), topped with ice cream, if desired.