Place honey, water, and balsamic vinegar in a pot and bring to a boil. Add the figs, simmer 3-4 minutes. Remove from heat.
In sterilized jars, add 1 sprig of thyme and the black peppercorns. Spoon the figs and liquid into each jar. Leave about 1/4 inch of headspace.
If canning, remove any air bubbles with a knife and hot water bath process for 10 minutes. You can also let cool and store in refrigerator for use within a week or two without processing.