Preheat an outdoor grill or grill pan to medium-high heat (approximately 400°F/200°C).

In a small bowl, whisk together the melted butter, honey, cinnamon, and salt until well combined.

Brush the cut sides of the peach halves generously with the honey-butter mixture.

Place the peaches cut-side down on the clean, lightly oiled grill grates.

Grill the peaches undisturbed for 4 to 5 minutes until distinct grill marks appear and the fruit begins to soften.

Carefully flip the peaches using tongs and grill for an additional 2 to 3 minutes until the skins are slightly charred and the fruit is tender.

Remove from the grill and serve immediately while warm, optionally topped with a dollop of mascarpone or vanilla ice cream.