Prepare the Beef:Heat the olive oil in a large pot or Dutch oven over medium heat. Add the beef stew meat and season with salt and pepper.
Brown the meat on all sides, which should take about 5-7 minutes.
Remove the beef from the pot and set it aside.
Sauté the Vegetables:In the same pot, add the chopped onion, garlic, carrots, and celery. Sauté the vegetables until they start to soften, about 5 minutes.
Add the Broth and Simmer:Return the beef to the pot. Add the beef broth, water, and diced tomatoes (with their juice).
Stir in the thyme, rosemary, and bay leaf (if using).
Bring the mixture to a boil, then reduce the heat to low and cover the pot.
Let the soup simmer for 1 hour, stirring occasionally.
Add the Potatoes and Green Beans:After 1 hour, add the diced potatoes and chopped green beans to the pot. Continue to simmer the soup for another 20-30 minutes, or until the potatoes are tender.
Add the Frozen Vegetables:Stir in the frozen corn and peas. Cook for an additional 5-10 minutes until the frozen vegetables are heated through.
Adjust Seasoning and Serve:Taste the soup and adjust the seasoning with more salt and pepper if needed. Remove the bay leaf if you used one.
Ladle the soup into bowls and serve hot.