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 continuously. Add the melon and saute until the melon starts to take on color, 1 to 2 minutes. 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.