Preheat your grill to medium-high heat. While the grill is warming up, slice your peaches in half and remove the pits. Brush the cut side of each peach half with a thin layer of melted butter or coconut oil to prevent sticking and encourage caramelization.
Place the peaches cut-side down directly onto the clean grill grates. Close the lid and cook for 3 to 5 minutes, or until the fruit has softened slightly and distinct grill marks appear. Carefully flip them over and cook for an additional 1 minute on the skin side just to warm through.
While the peaches are on the grill, place the Greek yogurt in a small bowl. Stir it vigorously for a few seconds to make it extra creamy. You can stir in a small drop of honey or vanilla extract at this stage if you prefer a sweeter base.
Remove the peaches from the grill and place two halves on each serving plate. Dollop a generous spoonful of Greek yogurt into the center of each peach. Drizzle the honey over the top, sprinkle with ground cinnamon, and add your optional garnishes like mint or nuts.