Season the beef with salt. Heat the oil in a large heavy pot over medium-high heat. When the oil is hot, but not smoking, add the beef cubes. Arrange them in a single layer and cook, undisturbed, for 3 minutes. Stir and cook for another 3 minutes, stirring occasionally. If needed, cook for 1–2 more minutes until the liquid evaporates and the beef sizzles, stirring constantly.
Lower the heat to medium and add the onion and celery. Cook for 2 minutes, stirring occasionally.
Add the garlic, tomato paste, Italian seasoning, and black pepper. Cook for 1 minute, stirring frequently.
Add the diced tomatoes and beef broth. Stir while gently scraping the browned bits from the bottom of the pot. Raise the heat and bring the broth to a simmer (about 5 minutes). Lower the heat to medium-low, cover, and cook for 10 minutes, stirring occasionally. Adjust the heat as needed to maintain a simmer.
Add the vermicelli noodles and raise the heat to bring the liquid back to a simmer. Lower the heat to medium-low, cover, and cook for 5 minutes, stirring often to prevent the pasta from sticking.
Add the mixed vegetables to the pot. Ensure the soup is simmering; if not, raise the heat slightly. Cover and cook for 5–7 minutes, stirring occasionally, until the pasta is tender. Keep the broth at a simmer, adjust the heat as needed.
Taste the soup and add more salt, if necessary. As a reference, we added an additional ½ teaspoon.
Serve with crusty bread or saltine crackers for dipping, or enjoy it on its own.