Preheat oven to 400°F (200°C).
- Boil potatoes or sweet potatoes until tender, about 15 minutes. Drain and mash with milk and butter or olive oil. Season with salt and pepper.
- While potatoes cook, heat olive oil in a large skillet over medium heat. Add onion, garlic, carrots, and celery; cook until softened.
- Add lean ground meat, breaking it apart, and cook until browned. Drain excess fat if needed.
- Stir in tomato paste, broth, Worcestershire sauce, thyme, salt, and pepper. Simmer for 5–7 minutes until slightly thickened. Stir in peas.
- Transfer meat mixture to a baking dish. Spread mashed potatoes evenly on top, using a fork to create texture.
- Bake for 20–25 minutes, until the topping is lightly golden.
- Let rest for 5 minutes before serving.