1. Rinse the figs, trim off and discard stems, and coarsely chop fruit. In a 1- to 2-quart pan over medium-high heat, combine figs, sugar, and 1 tablespoon water. Stir occasionally until mixture is boiling gently and figs turn shiny and darker, 3 to 5 minutes.
2. In a food processor or a blender, whirl fig mixture, olives, anchovies, capers, tarragon, and olive oil until coarsely puréed, scraping container sides as necessary. Scrape mixture into a small bowl.
Nutritional analysis per tablespoon.