Bring 5 quarts of water + 2 tablespoons of salt to a boil in a large pot. Add potatoes, reduce heat and simmer for 15-20 minutes, until just fork tender. Drain and rinse in cold water and set aside to cool.
Add shallots, celery, dill, and parsley to a large mixing bowl along with the potatoes. Pour dressing over the vegetables and toss gently to coat. Season with more salt and pepper if desired. Refrigerate potato salad for at least 1 hour before serving.