Melt the butter in a large pot over medium heat.
Add the carrots, celery, onion, and garlic. Cook until the vegetables are soft and fragrant (around 10 minutes).
Add flour and stir. Cook until golden (2-3 minutes).
Add the cooked chicken to the pot and stir together with the floured vegetables.
Add the 10 cups of broth to the pot. (If you prefer it to be more soup-like, add a little more broth; if you like a gravy/stew consistency, use less.)
Add the bay leaves.
Put the soup on high heat and bring to a boil. Season with salt to taste.
For the dumplings: In a bowl, combine 2 cups of flour, baking powder, salt, pepper and chives.
Add 3/4-1 cup of liquid (can also use milk, heavy cream, buttermilk, or chicken broth), and mix.
Scoop the dumpling dough dough out with an ice cream scoop, or just use your hands. Drop each rounded scoop of dough into the pot, trying not to let them touch.
Lower the heat to a low simmer, cover the pot, and allow to cook for 20 minutes.
Add peas (if using) and heat through.