Rinse beans in a colander. Leave in the sink to drain.
Chop onion. Heat oil a large saucepan over medium-low heat and add onion. Cook and stir occasionally while you continue.
Chop celery, grate or chop carrots, and mince the garlic, adding to onions and you complete each one. Cook and stir another 2 to 3 minutes. If using fresh cauliflower, chop now.
Stir in tomatoes, beans, and all remaining ingredients.
Keep covered, with lid ajar, and simmer on low at least 1 hour for best flavor. The flavors increase over time, so this is a great dish to make the day before and reheat before serving.
When ready to serve, adjust seasonings as desired.