Season the chicken thighs with salt and pepper and place them in a skillet over low heat. When the fat from the chicken begins to render out, raise the heat to medium. Cook for 4 to 5 minutes, flip, and cook for another 4 to 5 minutes. Remove the chicken thighs from the skillet and set aside. The thighs will be only partially cooked.

Add the onions, celery, and carrots to the skillet. Sprinkle a small amount of salt over the vegetables and sauté until the onions are translucent.

Add the dry Sherry to deglaze the skillet, scraping any browned bits from the bottom of the pan.

Transfer the vegetables and liquid from the skillet into a stockpot. Add the chicken wings, chicken broth, and the partially cooked chicken thighs and cook for about 30 minutes over medium heat.

Remove the chicken wings and thighs from the stockpot and allow them to cool. Leave the stockpot on the stove over medium heat.

While the chicken is cooling, prepare the dumplings: In a medium-sized bowl add the flour, sugar, salt, and baking soda and stir to combine. Add the half and half and melted butter and stir until the dough forms a ball. Shape the dough into golf ball–sized pieces and drop them into the stockpot.

Debone the chicken and return the meat to the stockpot. Cook for another 10 to 15 minutes until the dumplings are fully cooked and have increased in size.

If desired, sprinkle with fresh parsley before serving.