Add carrots, celery, onion, and garlic to a 6-quart slow cooker.
Place chicken thighs over the vegetables.
Season with thyme, parsley, poultry seasoning, black pepper, and salt.
Distribute butter over the chicken.
Pour chicken broth around the chicken.
Cover and cook on LOW for 5–6 hours or HIGH for 3–4 hours, until the chicken reaches at least 165°F (74°C).
Remove the chicken and shred it into bite-sized pieces.
Return shredded chicken to the slow cooker.
Stir in heavy cream.
Whisk cornstarch with cold water and stir into the chicken mixture.
Cover and switch the slow cooker to HIGH.
Whisk flour, baking powder, salt, and garlic powder together in a bowl.
Cut cold butter into the flour until coarse crumbs form.
Gently stir in enough milk to create a soft, slightly sticky dough.
Drop 10–12 portions of dumpling dough over the hot chicken mixture.
Cover immediately.
Cook on HIGH for approximately 45–60 minutes without repeatedly opening the lid.
Check that the dumplings are cooked through; their centers should reach about 200°F (93°C).
Taste and adjust the broth seasoning.
Serve chicken, vegetables, broth, and dumplings together.