Melt butter in a large Dutch oven over medium heat. Add diced onions, sliced carrots, and celery. Sauté until the vegetables are softened and onions are translucent, about 5–6 minutes. Stir in minced garlic and cook for 1 more minute for a fragrant base.

Add chicken to the pot and season with salt, pepper, and dried thyme. Cook until lightly browned, about 4–5 minutes, allowing the chicken to soak up all those wonderful flavors.

Sprinkle flour over the mixture and stir well. Cook for 1–2 minutes to eliminate the raw flour taste, then slowly pour in chicken broth while stirring. Bring to a gentle boil, then reduce to a simmer. Add peas and cook until the veggies are tender and chicken is cooked through.

Mix dumpling ingredients in a bowl by combining 1 ½ cups flour, baking powder, and salt. Stir in melted butter, milk, and chopped parsley until just combined into a sticky dough.

Drop spoonfuls of the dough into the simmering soup. Cover the pot and cook for 15 minutes without lifting the lid, allowing the dumplings to become fluffy and absorb the flavors.

Check dumplings for doneness after 15 minutes (they should be fluffy and fully cooked). Stir in whole milk or heavy cream to finish off the soup, adjusting seasoning to taste. Serve hot with a sprinkle of fresh parsley.