Quickly add ½ of the sauce to the drained pasta, and turn the heat to medium-low under the pot. With tongs or a large spoon and fork, continuously stir the sauce and the pasta together for the remaining quarter of cooking time. (For most pasta, this will be about 3 minutes.)
Once the first half of the sauce is completely incorporated into the pasta, add the remaining ½ cup of reserved pasta water, and the remaining half of the sauce.
Fold the water and sauce into the pasta with your tongs a few times, then add the peas, spinach, and parsley. The heat from the pasta will cook the peas through, and wilt the spinach.
At this point, the pasta has probably finished cooking. Taste, and turn the heat off if the pasta is cooked to al dente perfection. If it's not there yet, keep the heat on, and continue cooking and stirring for an additional 1-2 minutes.