In a large pot, add the potatoes and cover amply with cold water. Bring the water up to a boil and reduce to a simmer. Add a generous pinch of salt to the water and allow the potatoes to cook until tender when pierced with the tip of a knife, 15 to 20 minutes.
Pour the water and potatoes into a colander placed in the sink to drain off all of the water. Return the same pot to the heat and add the milk. Bring the milk to a simmer and gingerly add the potatoes back into the pot. Season with salt. Whisk in the stick of butter. Whisk until all of the ingredients meld together. Taste for seasoning. Remove from the heat.
Use the remaining 1 tablespoon butter to "grease" the sides and bottom of the baking dish. Add in the breadcrumbs and roll them around inside the dish so it creates a butter/breadcrumb topping.
Using a whisk (or an electric mixer fitted with the whisk attachment), whip the heavy cream until fairly firm. Season with salt.
With a rubber spatula, gently fold the whipped cream and about 1/2 cup Parmesan cheese into the mashed potatoes. Taste for seasoning. Transfer the potatoes to a baking dish and top with remaining Parmesan. Place in the center of the oven and bake, undisturbed, for 15 to 20 minutes. The top should be light brown from the cheese and the potatoes hot. Serve immediately.
Make sure the potato chunks are all relatively the same size to assure even cooking time.