Cut potatoes in halves and place in pot of boiling water. Reduce heat and simmer until tender, about 15 minutes.
Meanwhile, in blender or food processor, combine basil, olive oil, 3 Tbsp. Red Wine Vinegar, 6 Tbsp. pine nuts, 4 Tbsp. parmesan and garlic. Process until completely blended. Season to taste with salt and pepper.
Drain potatoes and cool slightly. With 1/4 tsp. measuring spoon, scoop out small amount from cut surface of each potato half to form shallow cup. Sprinkle with remaining vinegar and toss to coat.
Arrange potato halves on serving dish. Fill each with pesto and sprinkle with remaining pine nuts and Parmesan. Serve warm or room temperature.