Rinse the beans and soak in boiling water for one hour. Drain.
Grind the first two ingredients in a mortar and pestle (or food processor) with a dash of salt. Slowly add the extra virgin olive oil.
This is the "pistou" and can be poured in ice cube trays, frozen (pop out and put in a ziploc freezer bag to store in freezer) or use it the same day as you make it (It will fade in color if not frozen).
In a pot that holds 3 quarts, at least, saute the garlic in the olive oil for a minute or two.
Add the beans, salt and the stock.
Cover. Bring to a boil, then simmer for 30 minutes.
Uncover and check seasoning (I like to add fresh ground black pepper) and simmer for 15-25 minutes more (or until beans are just tender). Watch the liquid, adding more so that the beans are not ever dry.
When beans are tender, but hold their shape, stir in the pistou.