Dice peppers, dried and fresh tomatoes and add to the cooled pasta with the black olives, mix everything. Chop the basil and mix in about 2/3 of it as well. Season to taste with oil, vinegar, salt and pepper. Slice the parmesan over the top to taste and mix again.
Let the salad steep for at least 2 hours. Just before serving, season to taste again and fold in the remaining basil.