1In a small saucepan, combine the vinegar, sugar, figs and cinnamon stick or rosemary and bring to a simmer. Cook over low heat for about half an hour, until the figs are plump and the liquid is syrupy. If you like, dissolve the cornstarch in about 2 tsp. water and add it to the mixture to thicken it a little; bring back to a boil for at least 2 minutes to allow it to thicken and get rid of any starchy texture.
2Meanwhile, grill the sausages until almost cooked through; holding them with tongs, cut them in half lengthwise, then throw them back on the grill for a few minutes, cut-side down, until char-marked on the bottom.
3Serve each sausage half topped with a few figs and some sauce.