Preheat oven to 200°C (400°F).
In a large pan, cook minced beef over medium heat until browned. Drain excess fat.
Add onions, carrots, and garlic, and sauté for 5 minutes.
Stir in tomato paste, beef broth, Worcestershire sauce, thyme, salt, and pepper. Simmer for 10 minutes.
Meanwhile, boil potatoes until tender. Drain and mash with milk, butter, salt, and pepper.
Spread beef mixture evenly in a baking dish. Top with mashed potatoes and smooth with a spoon.
Sprinkle cheese (if using) on top.
Bake for 20-25 minutes, until golden brown.
Let it cool for 10 minutes before serving.