Place the potatoes in a large pot and cover with cold water. Bring to a boil and cook until tender, about 15 minutes. Drain well.
Return the potatoes to the pot. Add 3 tablespoons of butter, the milk, 1/4 teaspoon salt, and a pinch of pepper. Mash until smooth and set aside.
Heat the remaining tablespoon of butter in a large skillet over medium heat. Add the onion and carrots and cook until they begin to soften, about 5 minutes.
Add the garlic and cook for 1 minute. Add the ground lamb, breaking it up with a spoon. Cook until browned, about 8 minutes.
Stir in the tomato paste, stock, thyme, remaining salt, and pepper. Simmer until the liquid thickens slightly, about 5 minutes. Stir in the frozen peas and remove from heat.
Transfer the lamb mixture to a baking dish. Spread the mashed potatoes evenly over the top.
Bake at 400°F for 20 minutes until the topping is lightly golden. Let rest 5 minutes before serving.