Select peaches that yield slightly to gentle pressure. Cut each peach in half along the natural seam, and gently twist to separate halves. Remove the pit with a spoon or your fingers.
Preheat your grill to medium-high heat (approximately 375°F-400°F). Clean the grates thoroughly and oil them lightly to prevent sticking.
Brush the cut sides of the peaches with melted butter. For an extra flavor dimension, sprinkle a tiny pinch of sea salt over the buttered surface.
Place the peaches cut-side down on the preheated grill. Allow them to grill for about 3-4 minutes, until grill marks develop and the natural sugars caramelize.
Flip gently using tongs and grill for another 2-3 minutes until the skin side is lightly marked and the peaches are tender but still hold their shape.
While the peaches grill, mix the Greek yogurt or mascarpone with 1 tablespoon honey and the vanilla extract in a small bowl.
Transfer the grilled peaches to serving plates, placing them cut-side up. Top each peach half with a generous dollop of the yogurt mixture.
Drizzle with additional honey, sprinkle with chopped nuts if using, and garnish with fresh mint leaves. Serve immediately while still warm.