Step 1: Pat your beef dry with paper towels and season generously with salt and black pepper. In a large Dutch oven or heavy-bottomed pot, heat 1-2 tablespoons of olive oil over medium-high heat.
Step 2: Brown the beef in batches, ensuring not to overcrowd the pot. Sear until deeply browned on all sides, about 3-5 minutes per side. Remove the beef to a plate and set aside.
Step 3: Reduce heat to medium. Add a little more oil if needed, then add diced onions, carrots, and celery to the pot. Sauté for 5-7 minutes until the vegetables start to soften and the onions are translucent. Scrape up any browned bits from the bottom of the pot.
Step 4: Stir in minced garlic and cook for another minute until fragrant. Add tomato paste and cook for 2-3 minutes, stirring constantly, to deepen its flavor.
Step 5: Deglaze the pot with a splash of beef broth or a dry red wine, scraping up any remaining browned bits. Return the browned beef to the pot.
Step 6: Pour in the remaining beef broth, diced tomatoes (undrained), and Worcestershire sauce. Add dried thyme, bay leaves, and a pinch of red pepper flakes (optional, for a subtle kick). Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 1.5 to 2 hours, or until the beef is very tender.
Step 7: Add cubed potatoes and continue to simmer, covered, for another 20-30 minutes, or until potatoes are tender.
Step 8: Stir in frozen peas, green beans, and corn (or any other quick-cooking vegetables) and cook for an additional 5-10 minutes, or until heated through and tender-crisp.
Step 9: Taste and adjust seasonings. Add more salt, pepper, or herbs as needed. Remove bay leaves before serving.
Step 10: Ladle hot soup into bowls and garnish with fresh chopped parsley if desired. Enjoy your truly comforting vegetable beef soup!