Slice the fruit in half and remove the pits. Brush the cut side of the fruits with the oil.
Grill, cut-side down, for 30 seconds, then turn 90 degrees to create grill marks and grill another 30 seconds. Arrange peaches, cut-side up, on a serving platter. Spoon a dollop of yogurt over each half, then drizzle with honey. Garnish with mint and serve immediately.