Heat an indoor grill pan or outdoor grill over high heat. Brush the grates with oil.
Slice the melon into about 8 wedges that are at least 1-inch thick in the middle. Slice off and discard the rind, staying close to the fruit. Brush the cantaloupe with oil; season with salt and pepper. Grill the wedges about 2 minutes a side or until grill marks appear. If cooked much longer, the fruit will become too soft. Remove cantaloupe to a plate and allow to cool to the touch. If including figs, brush the cut side with oil and place them on the grill, cut-side down, for about 45 seconds or until grill marks appear. Remove and set aside.
When cantaloupe has cooled, wrap a slice of prosciutto around the middle of each wedge; arrange the wrapped wedges on a serving tray. Add the grilled figs around the tray, if using.
Instead of slicing the mozzarella, try tearing it. Grab hold of a corner of the cheese and pull; it will tear along it’s natural fault lines, not only giving the cheese a more rustic look, but also allowing it to soak up more flavor. Dot the mozzarella around the dish.
Sprinkle the chopped tarragon on top of the fruit and cheese, season with salt and pepper and finish with a drizzling of oil. Garnish with additional sprigs of fresh tarragon. Serve at room temperature.