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