Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the chopped onion, carrots, and celery. Sauté for 8-10 minutes, or until the vegetables have softened, stirring occasionally.

Stir in the minced garlic and red pepper flakes (if using) and cook for another 1 minute until fragrant. Pour in the sourdough discard and stir well to combine with the vegetables. Cook, stirring frequently, for 3-5 minutes. The discard will cook down and coat the vegetables slightly, and its sour notes will mellow.

Add the crushed tomatoes, vegetable broth, dried oregano, and dried basil to the pot. Stir to combine. Bring the soup to a gentle simmer, then reduce the heat to low, cover, and let it cook for 20-25 minutes, allowing the flavors to meld and the vegetables to become very tender.

Remove the pot from the heat. For a smooth soup, use an immersion blender to carefully blend the soup directly in the pot until it reaches your desired consistency. Alternatively, you can transfer batches to a regular blender (be cautious with hot liquids and blend in small amounts, venting the lid). If you prefer a chunkier soup, skip this step.

Stir in the salt and black pepper, tasting and adjusting seasoning as needed. If using, stir in the heavy cream or milk for a richer, creamier texture. Heat through gently for another 2-3 minutes if adding cream, but do not boil. Ladle the soup into bowls, garnish with fresh chopped basil, and serve hot.