Red wine sounds the perfect deep note to accompany the midrange flavor of figs.
Place peppercorns on a cutting board. Using the bottom of a small saucepan, crack peppercorns. Tie the thyme in a bundle with kitchen twine. Place peppercorns, dried figs, shallots, red wine, red-wine vinegar, thyme bundle, salt, and sugar in a medium saucepan. Set over medium-high heat, and bring to a boil.
Reduce the heat to medium low, and simmer until figs are soft and the liquid has thickened, about 45 minutes.
Remove and discard the thyme bundle. Stir in fresh figs. Cook, stirring frequently, until figs break down, 10 to 15 minutes. Remove the pan from heat.
Transfer to a large bowl set over an ice bath to chill; store in an airtight container, refrigerated, up to 4 weeks.
We used Calimyrna figs for this chutney, but the Black Mission variety can also be used.