Separate the legs into thighs and drumsticks; cut each breast half diagonally in half through the bone. If you wish, remove the skin. Sprinkle the chicken with:
Salt and ground black pepper or ground white pepper to taste
Heat in a heavy 8- to 10-inch skillet over medium heat until fragrant and golden:
4 tablespoons unsalted butter
Place as many chicken pieces in the pan as will fit comfortably and cook, turning once, until pale golden, 3 to 5 minutes on each side. Remove the chicken to a plate and brown the remaining pieces in the same manner. Add to the fat in the pan:
1 1/2 cups chopped onions
Cook, stirring occasionally, until the onions are tender but not browned, about 5 minutes. Stir in:
1/3 cup all-purpose flour
Cook, stirring, for 1 minute, then remove the pan from the heat and whisk in:
2 cups hot water
1 3/4 cups Chicken Stock
Whisking constantly, bring the mixture to a boil over high heat. Add:
3 medium carrots, peeled and diced (3 carrots yields 1 cup)
2 large or 3 medium diced celery stalks (2 to 3 stalks yields 1 cup)
1/2 teaspoon dried thyme
1 teaspoon salt
1/2 teaspoon ground black pepper or ground white pepper
Return the chicken pieces with all accumulated juices to the pan and bring to a simmer. Reduce the heat so that the liquid barely bubbles. Cover tightly and cook until the chicken is slightly undercooked and the dark meat pieces exude slightly pink juices when pricked with a fork, 15 to 20 minutes. (The chicken will cook further once the dumplings are added). Skim off the fat from around the sides of the pan with a spoon. If you wish, stir in:
1/4 to 1/2 cup heavy cream
Season to taste with:
Salt and ground white pepper or ground black pepper
Several drops of fresh lemon juice
Push the chicken pieces down so that they are submerged in gravy and drop in spoonfuls over the top:
Dumplings, or Cornmeal Dumplings
Cover and cook as directed for dumplings. Serve immediately.
