In a large microwave-safe bowl, heat chocolate in a microwave oven on full power (100%) until soft, about 2 minutes, stirring every 30 seconds.
To chocolate, add mascarpone, ricotta, 1/4 cup granulated sugar, egg yolks, rum, flour, and chopped chestnuts; stir until well blended.
In a bowl, with a mixer on high speed, beat egg whites until foamy. Gradually add remaining 2 tablespoons sugar and continue to beat whites until they hold stiff peaks. Gently fold whites into cheese mixture; scrape into cookie crust and spread level.
Bake in a 350° oven until filling is firm when pan is gently shaken and springs back when lightly touched in the center, about 30 minutes (20 minutes in a convection oven).
Cool on a rack about 20 minutes. Run a knife between cake and pan rim; remove rim. Let torte cool to room temperature, about 45 minutes; proceed, or chill airtight up to 1 day.
Sift powdered sugar over torte. If desired, decorate top with whole chestnuts spaced evenly around rim. Cut into wedges and serve with ice cream.
Cookie crust. In a food processor or blender, whirl about 45 vanilla wafer cookies (6 oz. total) until finely ground. Pour crumbs into a 9-inch cake pan with removable rim. Add 3 tablespoons melted butter or margarine, 1 tablespoon each honey and rum, 1 teaspoon vanilla, and 1/4 teaspoon ground cinnamon; mix well and press evenly over bottom and 1 inch up sides of pan.