Warm the butter in a Dutch oven or stockpot over medium heat, then add the onion, celery, and carrots and cook for 7 to 8 minutes. The onion should turn translucent and the vegetables should smell sweet and buttery.

Lower the heat, stir in the garlic, parsley, thyme, and poultry seasoning for 1 minute, then stir in the 2 tablespoons of flour for 1 minute before adding the broth and bay leaves. The flour should smell lightly nutty rather than raw; simmer the broth for 20 minutes, until the carrot rounds are tender.

Take out the bay leaves, season with salt and pepper, then add the cooked chicken and frozen peas (optional) and simmer for 5 minutes. Keep the broth at a steady, quiet bubble so the chicken warms through without becoming dry.

Combine the flour, baking powder, sugar, and salt in a medium bowl, cut in the butter, stir in the milk just until combined, and drop small spoonfuls of dough into the soup before covering the pot for 15 minutes without lifting the lid. The dumplings should puff and smell fragrant with herbs when the lid comes off; garnish with chopped fresh parsley or thyme.