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Add boiling water to gelatin mix in large bowl; stir 2 min. until completely dissolved. Stir in strawberries; set aside. Beat pudding mixes and milk in medium bowl; whisk 2 min; stir in 1 cup COOL WHIP.
Microwave dulce de leche in microwaveable bowl on HIGH 20 to 30 sec. or until thin enough to pour when stirred. Place half the cake in large clear serving bowl; drizzle with half the brandy. Cover with layers of half each of the strawberry and pudding mixtures; drizzle with dulce de leche.
Top with remaining cake, brandy, strawberry mixture, pudding mixture and COOL WHIP. Garnish with chocolate curls. Refrigerate 2 hours.