Arrange bread in a 13 by 9-inch dish coated with cooking spray.
Combine 1/2 cup goat cheese and next 6 ingredients (through egg whites) in a medium bowl, stirring well with a whisk. Pour milk mixture over bread; top with remaining 1/2 cup goat cheese. Cover saran wrap. Refrigerate for 8 hours or overnight.
Remove bread pudding from refrigerator; let stand at room temperature 30 minutes. Uncover and bake at 350 degrees for 40 to 50 minutes or until set and golden brown. Sprinkle with onions. 6 servings.