Depending on the size of your fryer, you may need to fry in batches. Small (1 quart) electric fryers can only do 2 pieces at once. You can deep-fry in the body of a pressure cooker on a gas stove, but do not fill it with oil beyond half of its volume.
Pour the oil into the fryer, and bring it to 350 degrees F. While the oil is coming up, dredge the chicken pieces in flour. Shake off most of the excess. Dip the chicken (one piece at a time) in the eggwash, coating the surfaces entirely. Dredge the chicken again in the flour.
Carefully, place the chicken - skin-side down - into the hot oil. Watch the progress. Turn the chicken, periodically. Fry for about 10 minutes. When the chicken begins to float and it cackles, it is finished.
Remove the chicken from the oil. Drain it on paper towels. Season with salt and black pepper - if desired.