Heat olive oil in a large pot over medium heat. Add the ground beef and cook until browned. Drain excess fat.
Add diced onion, carrots, and celery. Cook for 5–7 minutes until soft. Add garlic and cook for 1 minute.
Stir in tomato paste and cook for 2–3 minutes. Pour in beef broth and mix well.
Add Worcestershire sauce, thyme, bay leaf, salt, and pepper. Simmer for 15–20 minutes until the vegetables are tender.
Boil the potatoes in salted water for 10–12 minutes. Drain and mash with milk and butter until smooth. Season with salt and pepper.
Add frozen peas and corn to the soup and cook for an additional 5 minutes. Remove the bay leaf.
Ladle the soup into bowls and top with mashed potatoes. Sprinkle with shredded cheddar cheese if desired.
