Layer the onion, carrots, and celery in the bottom of your crockpot. Place the chicken on top, then pour over the chicken broth.
Sprinkle thyme, parsley, garlic powder, and pepper. Add a pinch of salt, but hold off on the final salting until you taste later.
Cover and cook on low for 6–7 hours, or on high for 3–4 hours, until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender.
In a separate bowl, whisk together self-rising flour, milk, melted butter, and a pinch of salt to form a thick batter—the dumpling batter should be spoonable but not too runny.
Carefully open the lid. Remove the chicken to a plate and shred or chop it into bite-sized pieces. Return the chicken to the pot and stir in the peas.
Drop spoonfuls of the dumpling batter onto the surface of the hot stew. Cover again and cook on low for an additional 25–30 minutes, until the dumplings are cooked through and fluffy.
Taste and adjust salt if needed. If the broth seems too thin, you can thicken it slightly by whisking a teaspoon of cornstarch with a tablespoon of cold water and stirring it into the pot; cook a few minutes more until the desired thickness is reached.