Place cubed 3 pounds Russet Potatoes in a large pot and cover with cold, heavily salted water. Bring to a boil and cook until fork-tender (15–20 minutes).
Drain the potatoes completely. Return them to the pot and add the 1/2 cup Heavy Cream, 4 tablespoons Butter, and 1/4 cup Parmesan Cheese. Mash or whip until perfectly smooth and fluffy. Season generously with 1 teaspoon salt and 1/2 teaspoon black pepper. Set aside.
Heat the 1 Tbsp Olive Oil in a large, deep skillet or Dutch oven over medium heat. Add the 1 cup Yellow Onion, 1 cup Carrot, and 1 cup Celery. Sauté until softened (5–7 minutes). Add the 4 cloves Garlic and cook for 1 minute until fragrant.
Add the 1.5 lbs Ground Beef and cook, breaking it up with a spoon, until fully browned. Drain off any excess grease.
Stir in the t2 Tbsp Tomato Paste and cook for 2 minutes. Sprinkle in the 1 tsp Dried Thyme and 1/2 tsp Dried Rosemary.
Pour in the 1.5 cups Beef Broth and 1 Tbsp Worcestershire Sauce. Bring to a simmer and cook for about 5 minutes, allowing the gravy to slightly thicken.
Stir in the 1 cup Frozen Peas. Taste the filling and add 1 tsp Salt and 1/2 tsp Black Pepper as needed. Remove from heat.
Preheat your oven to 400°F (200°C). Lightly grease a large casserole dish (e.g., 9x13 inch).
Spread the entire savory meat filling evenly across the bottom of the dish.
Carefully spoon the Parmesan mashed potatoes over the meat layer. Use a fork to create peaks and ridges on the potato surface.
Bake for 20–25 minutes, or until the potato topping is golden brown and the filling is bubbling hot around the edges.
Let the pie rest for 5 minutes before serving.