Place potatoes in a large microwave-safe bowl; cover with lid or plastic wrap. Note: If using plastic wrap, make sure plastic wrap is not touching any ingredients and poke one small hole in cover to vent. Microwave on high for 10 to 12 minutes or until potatoes are tender (cooking time may vary depending on microwave). Use oven mitts to carefully remove from microwave.
When cool enough to handle, cut potatoes in half or quarters and spray liberally with olive oil spray. Grill over high heat for 5 to 7 minutes, turning occasionally, until grill lines are apparent. Remove from grill and let cool.
Cut into bite-size pieces and place in a large bowl. Whisk together vinegar, oil, salt and garlic; pour over potatoes and toss lightly to coat. Season with pepper, then cover and refrigerate until ready to serve. Just before serving, toss with Parmesan cheese and basil, then sprinkle with pine nuts.