Preheat oven to 275 F. Arrange bread cubes on baking sheet. Bake until light golden and dry, about 10 minutes. Transfer baking sheet to rack; cool completely. Increase oven temperature to 350 F. Combine 3 cups whipping cream, 1 cup milk and 1/2 cup sugar in heavy large saucepan. Bring to simmer over medium heat, stirring until sugar dissolves. Remove from heat. Add 10 ounces white chocolate (about 1 3/4 cup ) and stir until melted and smooth. Whisk yolks and eggs in large bowl to blend. Gradually whisk in warm chocolate mixture. Place bread cubes in 2 quart glass baking dish. Add half of chocolate mixture. Press bread cubes into chocolate mixture. Let stand 15 minutes. Gently mix in remaining chocolate mixture. Cover dish with foil. Bake pudding 45 minutes. Uncover and bake until top is golden brown, about 15 minutes. Transfer pudding to rack and cool slightly. (Can be prepared 1 day ahead. Cover with foil and refrigerate. Rewarm covered pudding in 350 F oven for 30 minutes before serving.) Bring remaining 1/2 cup cream to simmer in heavy medium saucepan. Remove saucepan from heat. Add remaining 8 ounces white chocolate and stir until melted and smooth. Serve pudding warm with warm white chocolate sauce.