Preheat your oven to 350 degrees F and lightly grease a medium sized oven-safe casserole dish with non stick spray or butter.
In a bowl whisk together the milk, cream, eggs, salt, pepper, chives and rosemary.
Add the diced ham and stir through.
Cut the sourdough bread into thick slices and then into cubes about 1-inch square.
Add the bread to the egg mixture and gently toss making sure all of the bread cubes are being coated with the mixture.
Transfer the bread pudding to your prepared dish and gently pat down.
Spread out any heavy spots of ham or herbs.
Sprinkle with the Parmesan cheese
Bake in the oven uncovered for about 45 minutes or until the center feels slightly springy to the touch.