1. Put chicken in a deep pot or Dutch oven. Add water to cover, or use a mix of 1 qt chicken broth and any additional water needed to cover the chicken.
2. Add the salt, celery, and onion. Cover and simmer until tender (40 -60 min). Next add carrots, and continue to simmer until carrots are tender (about 20-30 min). Meanwhile, make cornbread or biscuits, see 6 below.
3. Drain and set aside the broth from chicken. Reserve about 3 cups for the gravy. Note: You can skim the fat and use the chicken fat instead of butter, or use a combination of the two to make .25 cup of fat needed later on.
4. Save the carrots but you can throw out the celery and onion. Remove skin and bones from the chicken pieces and break or cut the meat into about ½ to 1 inch pieces. Put meat back into the pot and pour the rest of the broth (minus the 3 reserved cups) back over the chicken in the pot to keep it hot.
5. Heat the .25 cup chicken fat, butter or fat/butter combo in a saucepan and blend in flour with a whisk. Cook 2 minutes & avoid browning. Gradually whisk in 2 cups of the chicken broth (there will be 1 cup left). Mixture may be quite thick. Gradually whisk in the 2 cups of half and half. Gravy should be thick and smooth, but you can thin it with more broth if necessary. Salt & pepper to taste. Using a slotted spoon, remove the chicken from the both with broth and add the chopped chicken and carrots to the gravy. Add the peas (and pearl onions if desired) and allow 5 -10 minutes for them to heat up.
6. Meanwhile, make a 9x9 pan of cornbread or cornbread waffles according to the package directions. (We use Jiffy Cornbread mix or Bisquick mix Drop Biscuits for this dish.)
7. Cut cornbread into 3” squares, cut squares (or biscuits) in half horizontally and place the two halves on a plate or shallow bowl. (If serving cornbread waffles, serve 1 waffle per person.) Ladle hot, creamy chicken on top and garnish with parsley.
Other alternatives: make baking powder biscuits instead of cornbread; add pearl onions.