Lightly grease a 20x30cm baking dish. In a medium bowl, mix together the Alfredo sauce and milk. Spread 1/4 cup of this sauce in the bottom of the baking dish. Then layer 1/3 of the potatoes over the sauce in the dish. Sprinkle with 1 tablespoon of Parmesan cheese and salt and pepper to taste.
In a separate medium bowl, combine the ham, broccoli and 1 1/2 cups of the cheddar cheese. Mix well and spread 1/3 of this mixture over the potatoes in the baking dish. Then top with another layer of potatoes, followed by the ham mixture, finally topping all with the remaining cheeses. Pour the remaining Alfredo sauce over it all.
Cover and bake in preheated oven for 45 minutes, then uncover, reduce heat to 180 degrees C and bake for additional 25 minutes or until potatoes are tender. Let stand 10 to 15 minutes before serving.