Cut chicken backs, necks and wings into 1-inch pieces.

For the broth: in a large pot, combine the chicken, onions, water, bay leaves and salt. Bring to a boil. Reduce heat to low and simmer, partially covered, until the chicken is tender, 45 minutes to 1 hour. Remove the chicken pieces and set aside. Discard the chicken backs, necks, and wings. When the chicken pieces have cooled, remove the meat from the bones in chunks and set aside. Discard the skin and bones. Strain the broth and discard the vegetables.

Prepare the dumplings: In a medium bowl, mix the flour, baking powder, and salt together. In a small saucepan over low heat, bring the butter and milk to a simmer. Stir the butter and milk mixture into the dry ingredients with a fork and stir until the mixture just comes together. On a lightly floured surface, roll the dough out to a 1/8-inch thickness. Cut into long strips 1-inch wide. Transfer to a large plate or baking sheet and cover with plastic wrap. Refrigerate until ready to use.

For the Chicken and Dumplings: In a large Dutch oven, melt the butter over medium heat. Add the celery, carrots, onion, Essence, the 1/2 teaspoon salt and the 1/2 teaspoon pepper. Cook until the vegetables are tender-crisp, about 10 minutes, then add the garlic and cook for 1 minute longer. Stir in the flour and cook until golden-brown, 3 to 4 minutes, scraping the bottom of the pan as needed with a wooden spoon. Whisk in the wine and the reserved chicken broth and simmer for 20 minutes, until thickened. Then add the reserved chicken meat, heavy cream, and peas.

Place the dumplings on top of the chicken mixture and gently stir them into the hot liquid. Cover and simmer until the dumplings are cooked through, about 10 minutes. Stir the dumplings as needed to prevent them from sticking to the bottom of the pot. Add the parsley and thyme. Serve in large soup bowls.