Preheat oven to 400°F (200°C).
In a large skillet, sauté diced onion, carrot, and minced garlic over medium heat until softened, about 5 minutes.
Add ground lamb to the skillet and cook until browned, breaking it up with a spoon.
Stir in tomato paste and Worcestershire sauce, cook for 2 minutes until fragrant.
Pour in beef or lamb broth, bring to a simmer, and cook until the liquid reduces slightly, about 10 minutes. Add peas during the last 2 minutes. Season with salt and black pepper.
In a bowl, mix mashed potatoes with butter and milk until creamy and smooth. Season with salt and black pepper.
Transfer the meat mixture into a baking dish, spreading evenly.
Top the meat layer with the mashed potatoes, spreading smoothly and creating peaks with a fork for browning.
Bake in the oven for 20-25 minutes or until the mashed potato crust is golden brown and crispy.
Let rest for 5 minutes before serving. Portion into squares or rounds and plate on plain white plates.