Preheat grill to medium heat.
Wash and dry your peaches and then slice them in half and remove the pit (see Recipe Note).
Brush the cut side of each peach half with melted butter and sprinkle it with brown sugar.
Grill, cut side down, for approximately 5 - 7 minutes.
Meanwhile, combine the feta, yogourt and honey in a small bowl and mix well until combined.
Your peaches are done when they are warmed through and they have been caramelized on the cut side, with grill marks.
Transfer your grilled peach halves to a serving platter, cut side up.
Fill the cavity of each peach half (where the pit used to be) with the feta mixture.
Garnish with the mint or basil if desired and drizzle with additional honey.
Serve immediately and enjoy!