Boil the potatoes in salted water until tender, about 15-20 minutes. Drain and mash with milk and butter until smooth. Season with salt and pepper. Set aside.
Preheat the oven to 200°C (400°F).
In a large skillet, cook the ground meat over medium heat until browned. Remove excess fat.
Add onions and carrots to the skillet and cook until softened. Stir in the tomato paste and cook for another 2 minutes.
Add the frozen peas and broth, bring to a simmer, and cook for about 10 minutes until slightly reduced. Season with salt and pepper.
Transfer the meat mixture to an ovenproof dish. Spread the mashed potatoes over the top. If using, sprinkle with grated cheese.
Bake in the preheated oven for 20 minutes or until the top is golden and crispy.