Place the the fig pieces with the lemon juice, zest, thyme, sea salt, and water in a large, nonreactive saucepan over medium-high heat and bring to a boil.
Add the honey and simmer the figs over moderate heat, stirring occasionally, until the fruit is soft and the liquid runs off the side of a spoon in thick, heavy drops, about 20 minutes.
Ladle the jam into six 1/2-pint jars, leaving 1/4 inch of space at the top. Close the jars and let cool to room temperature. Store the jam in the refrigerator for up to 3 months or process the jars in a boiling water bath for 10 minutes.
Variations: Substitute white port, Grand Marnier or your other favorite liqueur for the water. Substitute rosemary for the thyme. Substitute high quality white or red balsamic for the lemon juice.