Heat oven to 350°F. Spray 8-inch square (2-quart) glass baking dish with nonstick cooking spray. In medium bowl, combine eggs, milk, sugar and vanilla; beat well.
In sprayed baking dish, combine blackberries and bread; toss to mix. Pour egg mixture over top, pressing down bread until completely saturated.
Bake at 350°F. for 40 to 45 minutes or until golden brown and puffed in center. Cool 10 minutes.
While pudding is cooling, spoon ice cream into microwave-safe 4-cup measuring cup or bowl. Microwave on DEFROST for 3 to 4 minutes or until melted, stirring every minute.
Serve warm bread pudding in individual dessert bowls. Pour melted ice cream over each.