Pat the beef cubes dry with paper towels and season generously with salt and pepper. Heat olive oil in a large Dutch oven or stockpot over medium-high heat. Add the beef in a single layer (work in batches if necessary to avoid overcrowding) and sear on all sides until well-browned, about 5-7 minutes per batch. Remove the browned beef from the pot and set it aside on a plate.

Reduce the heat to medium. Add the chopped onion, carrots, and celery to the pot, scraping up any browned bits from the bottom with a wooden spoon. 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 tomato paste and cook for 1-2 minutes more, allowing it to deepen in color.

Return the seared beef and any accumulated juices to the pot. Pour in the beef broth and the undrained diced tomatoes. Add the bay leaves, dried thyme, and dried rosemary. Stir everything together.

Bring the mixture to a boil, then reduce the heat to low, cover the pot, and let it simmer gently for 1.5 hours. This long simmer is key to making the beef exceptionally tender.

Stir in the cubed potatoes. Replace the lid and continue to simmer for another 20 minutes, or until the potatoes are beginning to get tender.

Add the green beans, frozen corn, and frozen peas to the soup. Simmer uncovered for an additional 10-15 minutes, or until the potatoes and green beans are fork-tender.

Remove the pot from the heat and discard the bay leaves. Taste the soup and adjust seasoning with additional salt and pepper as needed. Ladle the hot soup into bowls and garnish with fresh parsley, if desired. Serve immediately.