Layer the base: Add onion, carrots, celery, and garlic to the slow cooker. Place chicken on top. Sprinkle in thyme, parsley, bay leaf, salt, and pepper.
Pour in the chicken broth.
Cook the chicken: Cover and cook on Low for 6–7 hours or High for 3–4 hours, until the chicken is fork-tender.
Shred the chicken: Remove the chicken to a cutting board. Shred with two forks into bite-size pieces. Discard the bay leaf.
Thicken the broth: In a small saucepan, melt the butter over medium heat.
Whisk in 2 tablespoons flour and cook 1 minute. Slowly whisk in the cream until smooth and slightly thickened, 2–3 minutes. Stir this mixture into the slow cooker.
Return chicken and add peas: Add the shredded chicken and frozen peas to the slow cooker.
Stir, taste, and adjust seasoning with salt and pepper.
Make the dumpling dough: In a bowl, whisk flour, baking powder, salt, and garlic powder. Cut in the cold butter with a pastry cutter or your fingers until crumbly. Stir in milk until a soft, sticky dough forms.
Don’t overmix.
Add dumplings: Turn the slow cooker to High. Drop heaping spoonfuls of dough (about tablespoon-size) onto the surface of the simmering stew, leaving space between them.
Steam the dumplings: Cover and cook on High for 60–75 minutes. Try not to lift the lid for the first 45 minutes.
Dumplings are done when puffed and cooked through in the center.
Finish and serve: Gently stir around the dumplings to thicken the broth, but don’t break them up. Garnish with parsley and serve hot.