Lightly brush each peach half with coconut oil and sprinkle evenly with the ground cinnamon and ground ginger.
Place peach halves flesh-side down on heated grill grate. Let cook 2-3 minutes until char marks appear, then flip and grill the other side for 2-3 minutes. If peaches are still very hard, flip and grill again on each side for an extra 1-2 minutes. Peaches should be softened enough to cut into with a spoon when finished.
Remove peach halves from the grill and place flesh-side up on a plate. Add dollops of whipped cream to the center of each half, and then sprinkle a additional ground cinnamon over the whipped cream. Serve immediately.