1. Preheat oven to 350°. Lay pita breads on two 12- by 15-inch baking sheets and bake until lightly golden and slightly crisp at the edges, 6 to 8 minutes.
2. While breads are still warm, brush with olive oil and rub generously with the cut sides of the garlic clove.
3. Rinse and stem figs. Cut lengthwise into 1/4-inch-thick wedges. Distribute wedges over breads. Crumble goat cheese over the top and drizzle with honey. Sprinkle with thyme leaves and salt and pepper to taste.