Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the ground lamb and cook, breaking it up with a spoon, until browned and cooked through, about 5 to 7 minutes. If needed, drain off excess fat.

Add the onion, carrots, and celery to the pot. Cook for 5 to 6 minutes, stirring occasionally, until the vegetables begin to soften.

Stir in the garlic, tomato paste, Worcestershire sauce, thyme, rosemary, salt, and black pepper. Cook for 1 minute until fragrant.

Sprinkle the flour over the mixture and stir well to coat the meat and vegetables. Cook for 1 to 2 minutes to remove the raw flour taste.

Gradually pour in the beef broth and water, stirring constantly to prevent lumps. Bring the soup to a gentle boil, then reduce the heat and simmer for 15 to 20 minutes, until the vegetables are tender and the soup has thickened slightly.

Stir in the frozen peas and cook for 2 to 3 minutes more until heated through.

In a separate bowl, combine the warm mashed potatoes, milk, and butter until smooth and creamy. If desired, thin with a little more milk for a spoonable texture.

Ladle the soup into bowls and spoon a generous dollop of mashed potatoes on top, or swirl the potatoes into the soup. Garnish with parsley, cheddar, or crispy fried onions if desired.