Prepare the Mashed Potatoes:

1. Place potatoes in a large saucepan, cover with cold water, and add salt. Bring to a boil.
2. Reduce heat and simmer for about 15 minutes until fork-tender.
3. In a small saucepan, heat the milk and butter together.
4. Drain potatoes and mash them with the warm milk and butter mixture.
5. Stir in parsley and Parmesan (if using). Season with salt and pepper to taste.

Prepare the Filling:

1. Heat olive oil and butter in a large skillet over medium heat.
2. Add diced onion, carrots, and celery. Cook for 10 minutes until softened.
3. Stir in garlic, mushrooms, salt, and oregano. Cook for another 5 minutes.
4. Add tomato paste and cook for 8 minutes, stirring occasionally.
5. Add ground beef and cook until browned.
6. Stir in beef broth, Worcestershire sauce, and black pepper. Let simmer for 5 minutes until thickened.

Assemble the Pie:

1. Preheat the oven to 375°F (190°C).
2. Spread the beef mixture evenly in a 2-quart baking dish.
3. Top with mashed potatoes, smoothing them out with a spatula. Use a fork to create ridges on top.

Bake the Pie:

1. Bake for 40 minutes, until the top is golden brown and edges are bubbling.
2. Let the pie rest for 10 minutes before serving.