In a heavy bottom dutch oven add olive oil, chopped onion, salt and pepper and saute over medium heat until the onions begin to soften. About 5-7 minutes.
While onions are sauteing, chop carrots and celery and add to the onions. Cook for 7 minutes or until vegetables begin to soften.
Add fennel seed, garlic, and parmesan rind (if using) and saute for 3 minutes.
Add 2 cans of tomatoes and basil and allow to simmer for 10 minutes, stirring occasionally.
Add 3 cups of the vegetable or chicken stock and bring to a boil.
After the soup has come to a boil, reduce to a low and simmer for 40 minutes or until the vegetables are tender.
Remove the parmesan rinds (if using) And add the soup in 2 batches to a blender and starting on low speed blend the soup for 10 seconds.
Increase the speed to high and blend for at least 30 seconds or until the soup is super silky and creamy.
Add creamed soup to a large bowl and begin the second batch in the blender.
Pour all the blended soup back into the dutch oven and turn heat to medium -low to low depending on your stove.
Add the rest of the stock, the Pernod (if using) and the white wine vinegar.
Season with more salt if needed and allow to cook for another 20 minutes or until the flavor is to your liking.
Serve and Enjoy!