Place a large pot over medium high heat. Heat olive oil and add the chopped onion and celery and cook, stir until the vegetables are soft, 3 to 4 minutes. Add the garlic and cook until fragrant. Add sieved tomato, vegetable stock, ½ teaspoon of salt and stir to combine. Simmer for 15 minutes.
Meanwhile, in a medium mixing bowl, combine the ground beef, eggs, Parmesan, bread crumbs, and 1/2 teaspoon of the salt, mix until thoroughly combined.
Divide meat into tablespoons and roll into smooth balls. Set the rolled meatballs aside on a plate.
Carefully add the meatballs to the simmering broth. Gently stir, so as not to break up the meatballs. Simmer for 20 minutes, or until meatballs are cooked through.
In a pan on medium high heat, melt butter and add the vermicelli and cook until golden in color. Add the vermicelli to the soup, stir well, and cook for 10 minutes. Serve.