Heat a large saute pan or wok over high heat. Once the pan is hot, add the olive oil, followed by the onion, and saute for 1 to 2 minutes, moving the pan continually. Add the melon and saute for another 1 to 2 minutes or until the melon starts to take on color. Add the basil, salt, and pepper and continue to cook for another minute. Add the vinegar to the pan and toss to combine. Pour mixture onto a serving platter, sprinkle with the cheese and pine nuts, and serve immediately.