Heat a large pot over medium-high heat and add the olive oil. Add the onions, celery, carrots and garlic. Sauté until soft and lightly browned. Add the tomato puree and add the tarragon, artichokes, black olives, capers and seasoning. Bring to a simmer then add the mussels. Cover with a tight-fitting lid and steam until all the mussels have opened.
Turn off the heat and shuck the mussels one-by-one. Pull them from the shells and add mussel meat back to broth. Discard any unopened mussels. Reheat and serve over your favourite pasta.
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