Preheat oven to 425F. Bring a large pot of water to a boil. Add ½ tsp salt and potatoes. Cook for 12-15 minutes until softened. Drain, and mash with milk, butter, remaining ½ tsp salt and chives. Set aside.
Heat olive oil in a large pan over medium heat. Add onion and carrot, cook for 5-7 minutes. Until slightly softened. Add ground lamb and ½ tsp salt, cook and crumble for 5 minutes until lamb is browned and almost fully cooked. Add garlic and tomato paste, cook another minute, until fragrant. Add red wine, and cook another minute. Stir in thyme and frozen peas.
Spoon lamb mixture into a an 8x8 or 9x9 square baking dish. Top with potatoes.
Bake in the oven for 15 minutes or until topping has started to brown around the edges.