Prep the base: Add onion, carrots, celery, garlic, bay leaf, salt, and pepper to the crockpot. Lay the chicken on top. Pour in the chicken broth.
Slow cook: Cover and cook on Low for 6–7 hours or on High for 3–4 hours, until the chicken is very tender.
Make a quick roux: About 30 minutes before serving, melt butter in a small skillet over medium heat.
Whisk in flour and cook 1–2 minutes until it smells nutty. Stir the roux into the crockpot to slightly thicken the broth.
Shred the chicken: Remove chicken to a plate, shred with two forks, and return it to the crockpot. Stir in the heavy cream and frozen peas.
Taste and adjust seasoning.
Mix the dumplings: In a bowl, whisk flour, baking powder, and salt. Cut in cold butter with your fingers or a pastry cutter until sandy with pea-size bits. Stir in milk, parsley, and thyme just until a soft, sticky dough forms.
Do not overmix.
Add dumplings: Drop heaping tablespoons of dough over the surface of the stew, leaving a little space between each. Aim for 10–12 dumplings.
Steam to finish: Cover and cook on High for 30–40 minutes. The dumplings should be puffed and cooked through in the center.
Avoid lifting the lid during the first 25 minutes so the dumplings steam properly.
Herb it up: Stir in parsley, thyme, and chives. Ladle into bowls and serve hot.