Preheat oven to 350°F (177°C). Butter a 9X13 inch baking dish; set aside.
In a large skillet, over medium heat, sauté onion (1/2 cup), carrots (3/4 cup), and celery (1/2 cup) in butter (1/4 cup) until tender. Add garlic (2 cloves) and continue to cook until fragrant, about 1 minute.
Sprinkle flour (1/2 cup), sugar (2 teaspoons), salt (1 teaspoon), poultry seasoning (1/2 teaspoon), thyme leaves (1 teaspoon), and black pepper (1/2 teaspoon) over sautéd vegetables and whisk constantly, continuing to cook until thickened, about for 1 minute.
Reduce heat and gradually stir in broth (3 1/3 cups) and bouillon (1 tablespoon) then bring to a boil. Cook and stir constantly until thickened, about 1 minute; reduce heat.
Stir in peas (1 cup) and cook for 5 minutes, stirring constantly. Stir in cooked chicken (4 cups) and Worcestershire sauce (1 teaspoon).
Pour into the prepared baking dish.
Make Dumplings:
In a small mixing bowl, combine baking mix (2 cups) and thyme leaves 91 teaspoons). Using a fork, stir in milk (2/3 cup) until moistened. Drop by tablespoonfuls into mounds over the top of the chicken mixture.
Bake, uncovered, in preheated oven for about, 30 minutes. Cover and bake 10 minutes longer or until a toothpick inserted in a dumpling comes out clean. Sprinkle with parsley (2 tablespoons) and serve.