Peel and cut the potatoes into chunks, then place them in a pot of salted water. Bring to a boil and cook until tender, about 15 minutes. Drain well and set aside.
While the potatoes cook, heat olive oil in a large skillet over medium-high heat. Add ground lamb and cook, breaking it apart with a spatula, until browned and fragrant, about 8 minutes.
Add diced carrots to the skillet and cook for another 5 minutes until they start to soften and release their sweetness. Pour in broth and stir, scraping up any browned bits from the bottom of the pan.
Stir in fresh thyme, season with salt and pepper, and simmer the mixture until the vegetables are tender and the liquid has reduced slightly, about 5 minutes. Add peas and cook for another 2 minutes. Remove from heat.
Return to the drained potatoes, mash them with butter, cream, salt, and pepper until silky and fluffy. Adjust seasoning to taste.
Preheat your oven to 200°C (390°F). Spread the meat and vegetable filling evenly in a baking dish.
Spoon the mashed potatoes over the filling, spreading evenly with a spatula or back of a spoon. Sprinkle grated cheese over the top.
Bake in the oven for 25-30 minutes until bubbling around the edges and the top is golden brown. For extra crispness, broil for 2-3 minutes, watching carefully.
Remove from the oven, let rest for 5 minutes, then serve hot, garnished with fresh herbs if desired.
