Preheat oven to 375 degrees. Place four 6- to 8-ounce ovenproof bowls on a baking sheet. Set aside.
Place chocolate and butter in a medium 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. Set aside.
In a medium bowl, with an electric mixer, beat egg whites and salt until soft peaks form. Still beating, gradually add remaining 2 tablespoons sugar; beat until mixture is stiff and glossy.
Using a rubber spatula, mix about 1/3 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 puddings were previously refrigerated. Serve, warm or at room temperature (puddings may sink as they cool), topped with ice cream, if desired.