Preheat an outdoor grill for high heat, and lightly oil the grate. Brush peach halves with canola oil.
Place peach halves on the preheated grill. Grill until tender and peach is warmed through, about 10 minutes. Place the hot peach on a plate skin-side down. Sprinkle with brown sugar, allowing the sugar to melt. Alternatively, use a small torch to caramelize the sugar. Serve each peach half with 2 scoops of vanilla frozen yogurt and gingersnap cookie crumbles sprinkled on top.