Preheat oven to 400°F. Use a tablespoon of softened butter along with a pastry brush to butter the bottom and sides of a Dutch oven. Set aside.
Add cold water and a heavy pinch of Kosher salt to a large stock pot. To the salted water, add the peeled and chunked potatoes. Add enough additional cold water to cover by 1-inch. Bring to a boil over medium-high heat and cook until fork tender. Drain potatoes and add back into stock pot. Place back atop hot burner and shake to intentionally dry the potatoes for 1 minute.
Pass the potato pieces through a ricer or food mill and into a large mixing bowl. Use the tines of a fork to incorporate 6 tablespoons of the unsalted butter as well as the whole milk. Salt and pepper to taste.
Using a stand mixer or a handheld electric mixer, whip heavy cream until soft peaks form. Use the fork tines to incorporate 1/3 of the whipped cream into the potatoes. Next, use a rubber spatula to fold in the remaining whipped cream VERY GENTLY. You want to keep the loftiness of the whipped cream, so be gentle while folding.
Scrape the potato mixture into the buttered Dutch oven and dot the surface with another tablespoon of butter cut into 6 small pieces. Use a microplane or cheese grater to grate a block of fresh Parmesan to where you have 1/2 cup and sprinkle that over the potatoes.
Place into the fully preheated oven, NO LID, for 25 minutes. At the end of the 25 minutes, turn on the broil element and broil the potatoes for 2 to 3 minutes or until a rich and golden-brown crust develops on the surface of the potatoes.
Remove the Dutch oven from your oven and allow to stand for 10 minutes before serving. As you serve, ensure each person gets a little bit of Parmesan crust with their potatoes.