Combine first 3 ingredients and 2 tablespoons vinegar in medium stainless steel bowl. Set bowl over pan of simmering water (do not allow bowl to touch water). Whisk until sabayon triples in volume and thermometer registers 160°F, 4 minutes. Place bowl over larger bowl filled with ice and water; whisk sabayon until cool.
Beat cream in another medium bowl to soft peaks. Add sabayon and fold together. Cover and refrigerate sabayon.
Puree 3/4 cup quartered berries with 2 tablespoons sugar and remaining 1 tablespoon balsamic vinegar in processor. Pour puree into large bowl. Add remaining berries and toss to coat.
Arrange 3 thin cake slices on each of 6 plates. Spoon berry mixture alongside. Top with sabayon and serve.
