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 it in one layer and cook, undisturbed, for 3 minutes. Stir well and cook another 3 minutes, stir occasionally. If necessary, continue cooking for 1-2 minutes until the liquid has cooked out and the beef is sizzling, stir constantly.
Then, lower the heat to medium and add the onions and celery. Cook for 2 minutes, stir occasionally.
Next, add the garlic, tomato paste, Italian seasoning, and black pepper to the pot. Cook for 1 minute, stirring frequently.
Add the diced tomatoes and beef broth. Stir while gently scraping the browned bits on the bottom of the pot. Raise the heat and bring the broth to a simmer it will take about 5 minutes). Then, lower the heat to medium-low, cover the pot and cook for 10 minutes, stir occasionally. Keep the broth at a simmer, raise or lower the heat as needed.
Add the vermicelli to the soup. Raise the heat, bring the liquid back to a simmer. Then, lower the heat to medium-low, cover and cook for 5 minutes. Stir often to make sure the pasta is not sticking to the bottom of the pot.
Lastly, add the vegetables to the pot. Check that it is simmering. If it is not raise the heat a bit. Cover and cook for 5-7 minutes until the pasta is tender. Stir occasionally and keep the liquid simmering; lower or raise the heat as needed.
Taste the beef noodle soup and add salt if needed. As a reference we added ½ teaspoon to ours.
Serve with crusty bread for dipping or saltine crackers. But there’s no need because this hearty soup is satisfying on its own.