In a large pot or Dutch oven, heat 1 tablespoon of the olive oil or butter over medium-high heat. Season the beef with seasoning salt.
Add the seasoned beef to the pot in batches (to avoid overcrowding) and sear until browned on all sides, about 3-4 minutes per batch. Add more oil or butter between batches if needed. Remove from the pot and set it aside.
In the same pot, add the remaining 2 tablespoons oil or butter. Once hot, add diced onion and cook 1 minute. Add fresh garlic, stir, and cook an additional minute.
Mix in celery and carrots, and cook 3-4 minutes, or until the onions are translucent and vegetables are slightly tender.
Add tomato paste and sprinkle flour over the vegetables. Stir to coat them evenly. Cook for 1-2 minutes, stirring constantly.
Gradually stir in beef broth or stock and water, scraping up any browned bits from the bottom of the pot.
Add bay leaves and thyme sprigs (or dried thyme).
Return the browned beef. Bring to a boil, then reduce the heat to low. Cover and simmer for 1 hour, or until the beef is mostly tender.
After the hour, add potatoes, cover and continue simmering for 30 minutes.
Add green beans and frozen peas. Continue to simmer, uncovered, for 10 minutes.
Taste the soup and adjust the seasoning with seasoning salt or salt and pepper as needed. Remove the bay leaves and thyme sprigs before serving.
Ladle the soup into bowls and serve hot, with your favorite soup sides.