Preheat the grill to 400 degrees F (medium high heat). Once it is hot, clean the grill grates with a grill brush, then lightly coat the grates with cooking oil to help prevent the peaches from sticking.

Pat the peach halves dry if they are very juicy. Using a pastry brush, coat the entire cut surface of each peach half with a thin, even layer of melted butter, including the area around the pit cavity.

Place the peach halves directly on the hot grill with the cut sides facing down, leaving a little space between them. Close the lid and cook without moving them for about 4 minutes. For crisscross grill marks, rotate each peach one quarter turn halfway through this cooking time, then leave it in place to finish searing.

Use tongs to gently flip each peach so the skin side faces down. Close the lid and cook for another 2 to 3 minutes. The peaches are ready when they are heated through, slightly softened, and easily pierced with the tip of a knife, but are still firm enough to hold their shape. Remove them from the grill before they become mushy.

Transfer the grilled peach halves to individual bowls or dessert plates, placing one peach half cut side up in each serving. Let them rest for about 1 minute, then add a scoop of cold vanilla ice cream to each peach. Serve immediately while the peaches are still warm and the ice cream is beginning to soften. Drizzle with hot honey, if desired.