Preheat your oven to 375°F (190°C).

Place potatoes in a large pot of cold, salted water and bring to a boil. Cook until tender, about 20 minutes.

Brown the lamb in a large skillet over medium-high heat, breaking it up as it cooks. Drain excess fat, leaving about 2 tablespoons in the pan.

Add onions, carrots, and celery to the lamb. Cook until vegetables are softened, about 8 minutes.

Stir in garlic, tomato paste, and thyme. Cook for another minute until fragrant.

Pour in beef broth and Worcestershire sauce, scraping up any browned bits from the bottom. Simmer until the liquid reduces by half.

Add frozen peas and season with salt and pepper. Remove thyme sprigs.

Drain the potatoes and return them to the pot. Add butter and warm milk, mashing until smooth.

Stir in the grated cheddar cheese until melted. Season with salt and pepper.

Transfer the meat mixture to a 9x13 baking dish. Top with the cheddar mash, creating peaks with a fork.

Bake for 25-30 minutes until golden brown and bubbling around the edges.