Preheat oven to 350°.
To prepare crust, place cookies in a food processor or blender; pulse until crumbs form. Add butter, 1 tablespoon sugar, and egg white; pulse 5 times or until combined. Press into bottom of an 8-inch springform pan coated with cooking spray. Bake at 350° for 8 minutes. Cool in pan on a wire rack.
To prepare walnuts, combine 3 tablespoons sugar, water, and cinnamon in a small saucepan over medium heat. Cook 1 minute, stirring constantly until sugar nearly dissolves. Stir in walnuts; cook 2 minutes. Remove from heat; spoon mixture onto wax paper or parchment paper. Cool until brittle. Break into small pieces. Set aside.
To prepare filling, spoon 1 cup ice cream into a chilled bowl. Stir in 2 tablespoons cocoa. Cover and freeze.
Place 3 cups of ice cream in a chilled bowl, and stir in chocolate. Cover and freeze 30 minutes. Spoon half of chocolate mixture into crust, spreading with a rubber spatula or wooden spoon. Freeze for 1 hour. Spread cocoa mixture over chocolate mixture; freeze 30 minutes. Spread remaining half of chocolate mixture over cocoa mixture. Cover and freeze overnight.
Place torte in refrigerator 30 minutes before serving. Uncover and dust with 1 tablespoon cocoa; sprinkle with candied walnuts.