Place broth, chicken, potatoes, carrots, celery, onion, bay leaves, salt, and pepper in a programmable pressure multicooker (such as Instant Pot). Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 12 minutes. (It will take 18 to 20 minutes for cooker to come up to pressure before cooking begins.) Carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). (This will take 2 to 3 minutes.) When cooking is finished, remove lid from cooker. Transfer chicken to a plate or bowl, and shred with 2 forks.

Preheat oven to 400°F. Melt butter in a medium saucepan over medium. Add flour; cook, whisking constantly, 1 minute. Slowly whisk in milk; cook over medium, whisking constantly, until mixture is thick and smooth, about 2 minutes. Remove from heat. Remove 1 cup of liquid from cooker, and gradually stir into milk mixture to thin mixture slightly. Pour milk mixture into cooker; add shredded chicken, peas, and thyme; stir to combine.

Spoon chicken mixture into a 13- x 9-inch baking dish coated with cooking spray. Arrange biscuits on top of chicken mixture. Place baking dish on a rimmed baking sheet lined with aluminum foil. Bake in preheated oven until biscuits are golden brown and chicken mixture is thick and bubbly, about 35 minutes. Remove from oven, and let stand 10 minutes. Garnish with additional thyme before serving.