Heat olive oil in a large skillet over medium heat. Add diced onion and cook for 5 minutes until soft. Stir in minced garlic and cook for 1 minute.
Add ground beef or lamb to the skillet, breaking it apart as it cooks. Brown for 7-10 minutes, then drain excess fat.
Stir in mixed vegetables, tomato paste, Worcestershire sauce, dried thyme, dried rosemary, and season with salt and pepper. Cook for an additional 5 minutes until vegetables are tender.
Peel and chop potatoes, then boil in salted water until fork-tender, about 15-20 minutes. Drain and mash until smooth.
Preheat oven to 400°F. Spread the meat and vegetable filling in a 9x13-inch baking dish. Top with mashed potatoes and sprinkle with cheddar cheese if desired.
Bake for 25-30 minutes until the top is golden brown and filling is bubbling. Let cool for 5 minutes before serving.