Heat oven to 350°F. Butter bottom and sides of 9-inch springform pan. Line outside of pan with heavy-duty foil.

Combine sugar and hot water in small bowl until sugar dissolves. Stir in espresso powder.

Melt 1 pound chocolate and butter in large heatproof bowl set over saucepan stuffed with 1 inch nearly simmering water (bowl shouldn’t touch water). Let stand until chocolate is nearly melted, stirring every now and then. Remove bowl from heat; stir until melted and smooth. Stir in espresso mixture. Let cool until barely warm, not hot.

Whisk in eggs one after the other, just until blended. Whisk in 1 tablespoon rum. Pour into springform pan. Place in large shallow roasting or broiler pan; add enough hot tap water to roasting pan to come 1 inch up sides of springform pan.

Bake 45 to 55 minutes or until cake is set and center doesn’t move when pan is tapped. Remove pan from water bath; remove foil. Cool on wire rack to room temperature, about 2 hours. Run thin knife around edge of pan before releasing sides.

Meanwhile, heat cream in small saucepan over medium heat until small bubbles form around edge. Add 6 ounces chocolate; remove from heat. Let stand 2 to 3 minutes or until chocolate is nearly melted; whisk until smooth. Stir in 1 tablespoon rum. Refrigerate 30 minutes or until frosting is of spreadable consistency, stirring every now and then.

Spread frosting over top of cake, swirling to decorate. Refrigerate until frosting is set. (Torte can be made 1 day ahead. Cover and refrigerate.) Serve at room temperature.