To heat the chicken stock, add it to a medium saucepan and bring to a slow simmer.

Heat the butter, season the chicken with salt, and brown:

In a large (8-quart or bigger) thick-bottomed saucepan, heat the butter or olive oil over medium-high heat. Pat dry the chicken and season with salt.

Brown the chicken pieces in stages, starting with the skin side down; this will render out the fat that will be used to make the stew later.

When the chicken has browned on both sides, take it from the big saucepan and turn off the heat. Remove and discard the chicken skin, then place the chicken in the saucepan of boiling stock.

Poach the chicken in the stock for about 20 minutes, or until it is well cooked.

Remove the chicken pieces and place on a tray to cool for a few minutes. When the chicken parts are cool enough to touch, remove the flesh off the bones and chop into 2-inch slices. Set aside.

Return the heat to medium-high in the big pot. When the pot is heated, add the onion, celery, carrot, and thyme and cook until tender but not browned, about 4 to 5 minutes.

Add the flour and whisk thoroughly. The flour will absorb some of the oil in the saucepan and cling to the bottom. Reduce the heat to medium-low and continuously whisk the flour vegetable mixture for 2 to 3 minutes. Don't let it burn.

Get a ladle ready, and keep the saucepan of boiling chicken stock close. Add the sherry to the flour-vegetable combination. It will splutter and lock up.

Add a ladle of boiling chicken stock and stir well. It'll be goopy. Add another ladle, followed by another, stirring constantly until the soup comes together.

Add the remaining chicken stock and leftover chicken meat. Increase the heat and bring to a simmer, then reduce to a soft simmer while you prepare the dumplings.

In a larger basin, whisk together the flour, baking powder, and salt. Add (optional) chopped fresh herbs. Add the melted butter and milk to the dry ingredients.

Gently stir with a wooden spoon until the mixture barely comes together. (Note: Do not overmix or your dumplings will be too thick.)

In a larger basin, whisk together the flour, baking powder, and salt. Add (optional) chopped fresh herbs. Add the melted butter and milk to the dry ingredients.

Gently stir with a wooden spoon until the mixture barely comes together. (Note: Do not overmix or your dumplings will be too thick.)

Drop heaping teaspoonfuls of dumpling batter into the bubbling stew, covering the whole top. (Remember that the dumplings will easily double in size while they cook.) Cover and boil for about 15 minutes, or until the dumplings are well cooked.

Once you've covered the pan, don't peek while the dumplings cook! To be light and fluffy, the dumplings must be steamed rather than boiling. The steam is released when you uncover the pan.

If the dumplings are not fully cooked after 15 minutes (test with a toothpick or skewer), cover the pan again and simmer for another 5 to 10 minutes.

Gently mix in the peas, parsley, and cream, if using. Add salt and pepper to taste. Ladle meat, sauce, veggies, and dumplings onto soup bowls. Take note that the stew will thicken as it sets.