Pat the beef cubes dry with paper towels and season them with 1 teaspoon of salt and 1/2 teaspoon of pepper. Heat the oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the beef in a single layer, working in batches if needed, and brown on all sides. Transfer the browned beef to a plate and set aside.
Reduce the heat to medium. Add the chopped onion, celery, and carrots to the same pot. Cook, stirring occasionally, until the vegetables have softened, about 6-8 minutes. Add the minced garlic and cook for another minute until fragrant.
Stir in the quartered potatoes, the can of undrained diced tomatoes, the beef broth, water, Italian seasoning, and the remaining 1 teaspoon of salt and 1/2 teaspoon of pepper. Bring the mixture to a simmer.
Once simmering, reduce the heat to low, cover the pot, and let it cook for 15 minutes, or until the potatoes are just starting to become tender when pierced with a fork.
Return the browned beef and any accumulated juices to the pot. Stir in the okra, corn, and zucchini. Bring the soup back to a simmer.
Cover and continue to cook on low for another 20-25 minutes, or until the beef is tender and all the vegetables are cooked through. The beef is done when it reaches an internal temperature of 145°F (63°C).
Remove the soup from the heat. Let it rest for at least 3 minutes before serving. Taste and adjust seasoning with more salt and pepper if needed.