In a large pot, heat the olive oil over medium heat. Add the ground beef, cook until browned, then set aside.
Add diced onion, carrots, and celery to the pot. Cook until softened, then add garlic and tomato paste. Stir and cook for 2–3 minutes.
Pour in beef broth, Worcestershire sauce, thyme, bay leaf, salt, and pepper. Simmer covered for 15–20 minutes until vegetables are tender.
Meanwhile, boil the potatoes until tender. Drain and mash with milk and butter, then season with salt and pepper.
Add frozen peas and corn to the soup, cooking for 5 minutes. Remove the bay leaf.
Serve the soup in bowls topped with mashed potatoes and sprinkle with cheddar cheese if desired.