Preheat oven to 350 degrees. Lightly butter a 1 1/2-quart tall-sided baking dish. Coat with sugar, tapping out excess. Set dish on a rimmed baking sheet.

In a large heatproof bowl set over a pot of simmering water, combine chocolate, vanilla, and 1/4 cup water. Stir until chocolate is melted and mixture is smooth, about 10 minutes. Remove from heat and let cool to room temperature, 20 minutes.

Stir egg yolks into cooled chocolate mixture until well combined. Set souffle base aside.

In a large bowl, using an electric mixer, beat egg whites and cream of tartar on medium-high until soft peaks form, about 2 minutes. Gradually add sugar and beat until stiff, glossy peaks form, about 5 minutes (do not overbeat).

In two additions, fold egg-white mixture into souffle base: With a rubber spatula, gently cut down through center and lift up some base from bottom of bowl. Turning bowl, steadily continue to cut down and lift up base until just combined.

Transfer mixture to dish, taking care not to get batter on top edge of dish; smooth top. Bake souffle until puffed and set, 30 to 35 minutes. (Do not open oven during first 25 minutes of baking.) Serve immediately.