To make the yogurt sauce, combine Greek yogurt, lemon juice, honey, and vanilla. Stir well and keep refrigerated. Reserve lemon zest for garnish when serving.
To grill the peaches, make sure grill grates are clean. Pre-heat grill and oil the grates while preparing peaches.
Cut both peaches in half and remove the pit. Place cut side up on a plate and brush each half lightly with oil, being sure to cover both the cut side and the outside of the peach. Sprinkle cut sides with cinnamon.
Place peach halves, cut side down, on grill grates. Close lid and grill on low heat for about 4 minutes. Open lid and carefully lift peaches from the grates and flip so the outside of the peach is on the grates. Close lid and grill for another 3 to 4 minutes or until peaches are softened but not mushy.
Remove from grill and cook slightly.
To serve, drizzle a little balsamic vinegar on the bottom of 4 dessert plates. Place one peach half on each plate. Top each with a dollop of the honey and lemon yogurt sauce and sprinkle lemon on top. Serve immediately.