Grate the zest from one of the oranges and place it in the bottom of a wide salad bowl. Without peeling, slice all the oranges about 1/4 to 3/8 inch thick. Squeeze the juice from the end slices into the bowl over the zest. Remove any seeds, then remove the peel from each slice by laying it flat and turning it as you take a series of straight downward cuts, leaving no white pulp. Place the peeled slices in the bowl. Separate the onion slices into rings and add to the bowl.
In a small bowl, whisk together 7 tbsp. of the olive oil, the vinegar, and some pepper. Pour this vinaigrette over the onion and orange slices. Toss gently, being careful not to break up the orange slices, until the oranges and onions are coated. Marinate for 30 minutes to 1 hour.
Heat the remaining 1/2 tbsp. of oil in a skillet; brown the pine nuts over medium heat until they are medium tan don't allow them to blacken. Wash and dry the basil. Chop the leaves if they are large; leave them whole if they are small. Just before serving, add the basil and pine nuts to the salad bowl, toss gently, and serve. salt to taste.