Melt 4 tablespoons butter in a large Dutch oven or heavy pot over medium heat. Add the onion, carrots, and celery, then cook for 5 to 7 minutes until the vegetables begin to soften.

Add the minced garlic and cook for about 30 seconds. Sprinkle in 1/4 cup flour and stir for 1 minute to form a light roux.

Gradually whisk in the chicken broth to prevent lumps. Add the salt, black pepper, and poultry seasoning, then bring the mixture to a gentle simmer.

Add the chicken, partially cover the pot, and simmer for about 18 to 25 minutes. Cook until the thickest part reaches 165°F and the chicken is tender.

Remove the chicken from the pot and shred or chop it into bite-size pieces. Return the chicken to the soup.

While the chicken cooks, whisk together the dumpling flour, baking powder, and salt. Cut in the cold butter until the mixture resembles coarse crumbs, then stir in the milk just until a soft, slightly sticky dough forms.

Bring the soup to a gentle, steady simmer and drop the dough into the pot by rounded tablespoons. Make each dumpling approximately 1 1/2 inches wide and leave space between them because they expand.

Cover the pot and simmer gently for 15 minutes so the dumplings steam properly. Remove the lid and cook for 3 to 5 minutes more, until the dumplings are cooked through.

Taste the soup and adjust the seasoning with more salt if needed. Garnish with chopped parsley and serve hot.