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" 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.

In a Dutch oven or heavy pot, melt the butter over medium heat. Whisk in the flour and cook until golden-brown, 3 to 4 minutes. While whisking, add the wine,  chicken broth, Essence, and thyme. Cook until thickened, about 5 minutes, then add the celery, carrots, and onion. Cook until the vegetables are tender-crisp, about 15 minutes. Add the chicken meat, cream, and peas. Season with salt (if necessary), and add black pepper, to taste.

Place the dumplings on top of the chicken mixture and gently stir into the hot liquid. Cover and simmer until the dumplings are cooked through, about 10 minutes. Gently stir in the parsley. Serve in large soup bowls.