Cook the potatoes in a large pot of boiling salted water until they are very tender, about 15 minutes. Drain; return the potatoes to the same pot and mash well. Mix in the milk and melted butter. Mix in the mozzarella and 25g of the Parmesan. Season, to taste, with salt and pepper.
Transfer the potatoes to the prepared baking dish. Stir the breadcrumbs and remaining 125g of Parmesan in a small bowl to blend. Sprinkle the breadcrumb mixture over the mashed potatoe. Recipe can be prepared up to this point 6 hours ahead of time; cover and chill.
Bake, uncovered, until the topping is golden brown, about 20 minutes.