Preheat oven to 375°F (190°C).
Brown ground lamb or beef in a skillet over medium heat.
Add onion and garlic and cook until softened.
Stir in flour and cook 1 minute.
Add tomato paste, Worcestershire sauce, broth, thyme, salt, and pepper.
Simmer 5–7 minutes until thickened.
Stir in peas and carrots and cook 2 minutes.
Spread meat mixture evenly in baking dish.
Mix mashed potatoes with butter and milk until smooth.
Spread mashed potatoes over meat layer and sprinkle cheese on top if using.
Bake 20–25 minutes until top turns golden.
Let rest 5–10 minutes before serving.