For sauce:

Bring cream, liqueur, sugar, and vanilla to boil in heavy medium saucepan over medium-high heat, stirring frequently. Mix cornstarch and 2 teaspoons water in small bowl to blend; whisk into cream mixture. Boil until sauce thickens, stirring constantly, about 3 minutes. Cool, then cover and refrigerate until cold, about 2 hours. (Can be made 3 days ahead. Keep refrigerated.)

For bread pudding:

Combine bread, chocolate, and white chocolate in large bowl; toss to blend. Using electric mixer, beat eggs, 1/2 cup plus 2 tablespoons sugar, and vanilla in another large bowl to blend. Gradually beat in 1 1/2 cups cream and milk. Add cream mixture to bread mixture; stir to combine. Let stand 30 minutes.

Preheat oven to 350F. Spray 13x9x2-inch glass baking dish with nonstick spray. Transfer bread mixture to prepared dish, spreading evenly. Drizzle with remaining 1/2 cup cream. Sprinkle with remaining 2 tablespoons sugar. Bake pudding until edges are golden and custard is set in center, about 1 hour. Cool pudding slightly.

Drizzle bread pudding with sauce and serve warm.