Melt the butter over medium heat in a large Dutch oven. Add the celery & onion and saute until soft (5-8 minutes).
Add the chicken to the Dutch oven. Pour in the chicken broth. (The chicken should be completely submerged in the broth. If it isn’t, add more broth or water until covered.) Season with salt & pepper. Cover & simmer for 30 minutes.
Remove the chicken from the Dutch oven. Shred the meat and discard the bones. Return the shredded meat to the Dutch oven. Add the peas and cook for 5 minutes.
In a medium bowl mix together the milk & Bisquick. Drop dough by large spoonful into the Dutch oven. Cook (uncovered) for 10 minutes. Cover the Dutch oven and cook for an additional 10 minutes.