Season the chicken with the salt and pepper and place it in a 6-quart slow cooker with the onion, carrots and celery.
Add the broth, thyme and bay leaf, cover and cook on low until the chicken reaches 175°F, 5 1/2 to 6 hours.
Transfer the chicken to a plate, shred it into bite-size pieces and discard the bay leaf.
Melt the butter in a saucepan, whisk in the flour for 1 minute, then slowly whisk in the milk and 1 cup cooking broth.
Cook until the sauce coats a spoon, 4 minutes, then stir it into the cooker with the chicken and frozen peas.
Cover and cook on high until the peas are hot and the filling bubbles at the edge, 15 to 20 minutes.
Bake the biscuits according to the package until well browned, split them and set one over each bowl of filling.