Peel potatoes. Cut into equal chunks.
Boil potatoes until fork-tender, about 15 minutes.
Heat Dutch oven over medium-high heat.
Brown ground lamb completely, breaking apart.
Add onions and carrots to pot.
Cook vegetables until softened, 5 minutes.
Stir in garlic and tomato paste.
Pour beef broth into pot slowly.
Add thyme, salt, and pepper.
Simmer soup for 10 minutes total.
Drain cooked potatoes thoroughly.
Mash potatoes with butter and milk.
Add frozen peas to soup.
Cook 2 more minutes until heated.
Serve soup topped with mashed potatoes.