Asian Five-Spice Chocolate Cake

Preheat oven to 350 °F. Butter a 10- by 2-inch round cake pan. Line bottom with a round of parchment paper and butter the paper. Put chocolates in a large shallow bowl. Bring water, 1/2 cup sugar, and spice to a boil, stirring until sugar is dissolved, then pour through a fine sieve set over chocolates. Stir until smooth, then stir in butter until smooth. Beat eggs with remaining 3/4 cup sugar until increased in volume and pale and beaters leave a distinct trail (4 to 5 minutes in a standing mixer or 15 to 20 with a hand-held). Stir 1/4 of eggs into chocolate to lighten and fold in remainder gently but thoroughly (fold 1 to 2 minutes). Pour batter into pan and smooth top. Put pan in a water bath and bake in middle of oven 40 to 45 minutes, or until a tester inserted in center comes out with moist crumbs adhering. Remove from water bath and cool 2 hours in pan on a rack. Unmold cake by running a thin knife around edge, then heating pan 5 to 10 seconds on burner set at moderately low. Invert cake plate over pan and flip cake onto plate. (If cake sticks, tap bottom of pan with a knife handle. If that doesn't work, heat pan again.) Peel off paper. Serve cake in thin slices.