Load the slow cooker: Add the onion, carrots, celery, and garlic to the bottom of a 6-quart slow cooker. Place the chicken on top. Pour in the chicken broth and add the cream of chicken soup, thyme, parsley, bay leaf, pepper, and salt.
Stir gently to combine around the edges, leaving the chicken mostly covered.
Cook low and slow: Cover and cook on Low for 6–7 hours or High for 3–4 hours, until the chicken is tender and easily shreds.
Shred the chicken: Remove the bay leaf. Transfer the chicken to a plate and shred with two forks. Return the chicken to the slow cooker and stir.
If using, add the heavy cream and peas now.
Make the dumpling dough (scratch option): In a bowl, whisk flour, baking powder, and salt. Cut in the cold butter with your fingertips or a fork until the mixture looks like coarse crumbs. Stir in the milk just until a soft dough forms.
Do not overmix.
Add dumplings: Drop tablespoonfuls of the dough over the surface of the stew, or add biscuit pieces in an even single layer. Do not stir.
Steam the dumplings: Cover and cook on High for 45–60 minutes until the dumplings are puffed and cooked through. Avoid lifting the lid in the first 30 minutes so the dumplings can steam properly.
Finish and taste: Gently press one dumpling with a spoon to check doneness; it should be set and fluffy inside, not doughy. Taste the broth and adjust salt and pepper as needed.
Ladle into bowls and serve hot.