Heat olive oil in a large pot over medium-high heat. Add the beef stew meat and cook for 5-6 minutes, or until browned on all sides. Remove the beef and set aside.
In the same pot, add the onion, garlic, carrots, and celery. Sauté for 5-6 minutes, or until the vegetables are softened.
Return the beef to the pot and stir in the beef broth, water, diced tomatoes, potatoes, thyme, parsley, and smoked paprika. Bring the soup to a boil.
Reduce the heat to a simmer, cover, and cook for 45-50 minutes, or until the beef is tender and the potatoes are cooked through. Add more water if needed for desired consistency.
Stir in the green beans, corn, and peas. Simmer for an additional 10-15 minutes until the vegetables are tender.
Season with salt and pepper to taste. Serve hot, garnished with fresh parsley if desired.