Add the warm heavy cream, softened butter, and Parmesan. Whip or mash until smooth and fluffy. Season with the salt and pepper. Set aside.

Heat the olive oil in a large cast iron skillet or Dutch oven over medium heat. Add the onion, carrot, and celery and cook 6 to 7 minutes until soft.

Add the mushrooms and cook 4 to 5 minutes until their liquid has released and evaporated. Add the garlic and cook 1 minute more.

Add the ground beef and cook, breaking it up, until browned through. Drain off the excess grease.

Stir in the tomato paste and cook 2 minutes. Sprinkle the flour over the mixture and stir 1 minute until no dry flour remains.

Pour in the beef broth and Worcestershire sauce, scraping the bottom of the pan. Add the thyme and rosemary. Simmer 5 to 7 minutes until the gravy coats a spoon.

Stir in the zucchini and cook 3 minutes, then add the frozen peas. Taste and season with the salt and pepper. Remove from heat.

Heat the oven to 400°F. If needed, transfer the filling to a greased 9x13-inch baking dish and spread evenly.

Spoon the Parmesan mashed potatoes over the filling, spreading all the way to the edges to seal. Comb a fork across the surface to create ridges.

Bake 25 minutes, until the topping is golden and the filling bubbles at the edges. For a darker crust, broil 1 to 2 minutes, watching closely.

Rest 5 to 10 minutes before serving.