In a large Dutch oven or pot, melt butter and add the celery and onions. On low heat, sauté until the onions become translucent, about 5 minutes.
Add garlic and thyme and sauté 1 minute longer.
Stirring constantly, sprinkle flour over the vegetables and cook for 2 minutes.
Slowly add in the chicken broth stirring constantly.
Add the poultry seasoning, carrots, and potatoes.
Place lid on top, cook on medium heat until carrots and potatoes are slightly tender but not fully cooked, about 10-15 minutes.
Taste for seasonings. Add salt and pepper as needed.
Add cooked chicken and frozen peas.
Bring the stew back to a slow boil and make the dumplings.