Season the beef with the salt and pepper and brown it in two batches in the oil over medium-high heat, 5 to 6 minutes per batch.
Transfer the beef to a 6-quart slow cooker and add the onion, carrots, celery, mushrooms and barley.
Whisk the broth, tomato paste, Worcestershire and thyme and pour it into the cooker; tuck in the bay leaf.
Cover and cook on low until the beef is tender and the barley is cooked through, 7 to 8 hours.
Discard the bay leaf and stir in the frozen peas.
Cover and cook on high until the peas are hot and bright green, 8 to 10 minutes.
Thin the stew with 1/2 cup hot water if the barley has absorbed more broth than you like, then check the salt.