Cut the peaches in half and remove the pit: With a sharp paring knife, slice each peach in half. Then twist each half in opposite directions to pull the halves apart. Use your fingers to remove the pit. If it's stuck, carefully slide the knife under the pit and then pull it away.
Brush the peaches all over with melted butter.
Place the peaches, cut side down, on the grill. Grill until tender and slightly charred, about 4 minutes per side. Serve immediately.
Video
Notes
If you don't own a grill and would like to make this recipe, you can use a grill pan. Or, if you have a broiler-safe dish, you can broil the peaches for 3-4 minutes per side. Check on them often, to make sure they don't burn. I suggest you start checking on them after 2 minutes. And position the rack 6 inches below the flame, not directly below.