Put garlic in a food processor and whirl to mince. Add remaining ingredients and pulse into a chunky purée.
*To boil quail eggs, put eggs in a pot with water to cover by 2 in. Bring to a boil, then simmer 5 minutes. Drain eggs and transfer to a bowl of ice water to cool.
Make ahead: Tapenade, up to a month, chilled. Vegetables (except endive, which tend to brown so prep a couple of hours beforehand) and eggs, 1 day, chilled.
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