Toast the walnuts in a small nonstick skillet, stirring frequently. As soon as they become fragrant and begin to brown, add honey; cook over medium heat until honey is hot. Remove from heat; keep warm.
Cut the fruit in half and remove pit. Brush the fruit with the oil, place on the grill cut side down and cook until golden brown and caramelized, about 2 minutes. (Note: the fruit may be threaded on greased metal skewers.).
Turn the fruit over and continue cooking until just warmed through, about 2 minutes longer.
Remove the fruit from the grill and place 3 halves on each plate. Top each half with some yogurt and drizzle the honey-walnut mixture over the top. Garnish wish a mint sprig, if desired.