Preheat oven to 375°.
Combine figs and water in a small saucepan over medium heat. Cook 5 minutes, stirring frequently until liquid is absorbed. Place figs in a small bowl. Stir in olives, vinegar, oil, thyme, and pepper. Top each muffin half with 2 tablespoons cheese and 2 tablespoons fig mixture. Place muffin halves on a foil-lined baking sheet. Bake at 375° for 15 minutes or until cheese melts. Cut each muffin half in half. Garnish with thyme sprigs, if desired.