Sauté Aromatics: In a large pot, heat the olive oil over medium heat. Add the chopped onion and minced garlic, and sauté until softened and fragrant, about 5 minutes.
Add Tomatoes: Add the diced tomatoes to the pot, along with the dried oregano and basil. Stir to combine, and cook for another 5 minutes to allow the flavors to meld.
Simmer Soup: Pour in the vegetable or chicken broth, and season with salt and pepper to taste. Bring the soup to a simmer, then reduce the heat to low. Cover the pot and let the soup simmer gently for about 20-25 minutes, stirring occasionally.
Blend (Optional): For a smoother texture, use an immersion blender to puree the soup directly in the pot until smooth. Alternatively, transfer the soup in batches to a blender and blend until smooth. Be cautious when blending hot liquids.
Adjust Seasoning and Serve: Taste the soup and adjust the seasoning with salt and pepper if needed. Ladle the hot soup into bowls, garnish with fresh basil leaves if desired, and serve with croutons or bread on the side.