Cut the peaches in half and remove the seed, being careful not to tear the flesh. Place in a bowl with cinnamon sticks and enough cold water to cover them completely. Soak the peaches for 20 minutes then remove and pat dry with a paper towel.
While the peaches are soaking, mix the yogurt topping by stirring together the yogurt, honey, and almond extract until well-combined. Set aside in the fridge to chill. This can also be done a day ahead of time, if you prefer.
Once the peaches have soaked, melt the coconut oil and stir in the cinnamon.
Preheat the grill or grill pan to medium heat, about 325 - 375°F. (You can test this by how long you can hold your hand over the grill without it getting too hot. At medium heat, you should be able to hold your hand over the grill—about 5 inches off—for about 6-7 seconds before it feels too hot.)
Brush the cut side of the peaches with the cinnamon oil and place the peaches on the grill at a 45° angle. If your peaches aren’t touching the grill, you can place a heavy object, like a cast iron pan on the peaches for about 30 seconds to get the sear. Cook for about 2.5 - 3 minutes, or until the peaches are start to soften and are fairly easily coming away from the grill.
Turn the peaches over and grill for another 3 minutes, or until soft, but not too soft.
Serve with honey almond yogurt.