Heat a large skillet over medium heat. Add the ground beef or lamb and cook for 5-7 minutes, breaking it apart as it browns. Drain excess fat. Add diced onion and minced garlic, sauté for 3-4 minutes until translucent. Stir in mixed vegetables, tomato paste, Worcestershire sauce, beef broth, dried thyme, salt, and pepper. Simmer for 5-7 minutes until thickened.

Boil about 2 pounds of potatoes until tender. Drain and return to pot. Add butter, milk, salt, and pepper. Mash until smooth and creamy.

Spread the meat filling evenly in a 9x13-inch baking dish. Spread mashed potatoes over the meat mixture. Optionally, sprinkle shredded cheddar cheese on top.

Preheat oven to 400°F (200°C). Bake the assembled Shepherd's Pie for 25-30 minutes until the top is golden brown and edges are bubbling. Let cool for 5-10 minutes before serving.