Peel and quarter the russet potatoes, then place them in a pot of salted water. Bring to a boil and cook for 15-20 minutes until fork-tender. Drain, return to pot, and mash with warm milk, butter, and salt until smooth.

In a skillet, heat oil over medium heat. Add ground beef or lamb, breaking apart as it cooks. Sauté for 5-7 minutes until browned, then drain excess fat.

Add diced onion, minced garlic, and chopped carrots to the skillet. Cook for 5-7 minutes until onions are translucent and carrots soften.

Stir in frozen peas and cook for 2 minutes. Sprinkle flour over the mixture, stirring for 1 minute. Gradually add beef broth and tomato paste, simmer for 3-5 minutes.

Add Worcestershire sauce and dried thyme, along with salt and pepper to taste. Stir to combine and let flavors meld over low heat.

Grease a baking dish and spread the meat filling evenly. Spoon mashed potatoes on top, creating decorative peaks with a fork.

Preheat oven to 400°F (200°C) and bake for 20-25 minutes until bubbly and golden brown. Broil for 2-3 minutes for extra crispiness.

Remove from oven and let rest for 5-10 minutes before serving.