Brown the Beef: In a large pot, heat the olive oil over medium heat. Add the beef stew meat and brown it on all sides. This takes about 5-7 minutes.
Add Veggies: Toss in the chopped onions, garlic, carrots, celery, and potatoes. Cook, stirring for another 5 minutes until they soften a little.
Add the Broth and Tomatoes: Stir in the beef broth, diced tomatoes, and tomato paste. Add the bay leaf, salt, and pepper to taste.
Simmer the Soup: Bring everything to a boil, then reduce the heat to low. Cover and let it simmer for about 30-40 minutes, until the vegetables are tender.
Add the Green Beans, Corn, and Peas: Stir in the green beans, corn, and peas. Continue to cook for another 10 minutes.
Serve: Remove the bay leaf, taste the soup, and adjust seasoning if needed. Ladle the soup into bowls, and if you like, garnish with fresh parsley.