1. **Prepare the mashed potatoes:** Place potatoes in a large pot and cover with water. Bring to a boil over medium-high heat, then reduce heat and cook until fork-tender, about 15 minutes. Drain, then add milk, butter, salt, and pepper. Mash until smooth and creamy. Set aside. 2. **Make the filling:** In a large skillet over medium heat, cook ground beef or lamb until browned. Drain excess fat if necessary. Add onion, garlic, and carrots; cook for 5-7 minutes until softened. 3. Stir in frozen peas, broth, tomato paste, Worcestershire sauce, dried thyme, salt, and pepper. Simmer for 10-15 minutes until the mixture thickens slightly. 4. **Assemble:** Preheat oven to 400°F (200°C). Transfer the meat and vegetable mixture to a 9×13-inch baking dish or deep pie dish. Spread mashed potatoes evenly over the top. 5. **Bake:** Bake for 25-30 minutes, until mashed potatoes are lightly golden and filling is bubbling around the edges. 6. **Serve:** Let cool for a few minutes before serving. Garnish with chopped parsley if desired.