Cook pasta in a large pot of salted water until al dente. Drain. Rinse with cold water until the pasta reaches room temperature. Set aside.
In a blender or food processor, puree the basil, Parmesan, garlic, pine nuts, salt, pepper and olive oil until smooth.
Grill or boil the corn. If boiling, set the corn into a large pot of cold water. Bring just to a boil, then remove from heat. Using a sharp knife, shave the kernels off the cobs and discard.
Toss the pasta with the pesto sauce in a large bowl. Fold in the remaining ingredients. Cover and chill until ready to serve.