In a small bowl whisk together vinegar, honey, cinnamon and salt. Set aside.
Carry dough, olive oil, peaches and goat cheese out to the grill.
Brush olive oil liberally on one side of each dough round. Place oil-side down on grill grates. Close lid and let cook for 1-2 minutes, or until large bubbles start to form.
Brush olive oil on top side and then flip crusts over.
Evenly distribute the peaches and goat cheese (in dollops) over the pizzas. Close grill lid, turn to low and let goat cheese met for 2-3 minutes.
Remove from grill, sprinkle with thyme and drizzle with balsamic-honey sauce. Cut into slices and serve immediately.