Pat chicken dry, season with salt and pepper, and cut into 1-inch pieces if using breasts.
Heat olive oil in a large Dutch oven over medium-high heat. Add onion, carrots, and celery, cooking for 5-7 minutes until softened.
Add garlic and cook for 30 seconds. Add butter, melt completely, then whisk in flour and cook for 2-3 minutes until golden.
Slowly whisk in chicken broth followed by milk. Add thyme, sage, rosemary, bay leaves, Worcestershire sauce, salt, and pepper. Bring to a gentle boil, then reduce heat to medium-low.
Add seasoned chicken, cover, and simmer for 15-20 minutes until chicken reaches 165°F (74°C). Remove chicken, shred if needed, and return to pot.
Whisk flour, baking powder, salt, and garlic powder in a bowl. Cut in cold butter until pea-sized. Add milk and stir just until combined. Mix in parsley if using.
Remove bay leaves from simmering soup. Drop rounded tablespoons of dough onto the surface, spacing them about 1/2 inch apart.
Cover with a tight-fitting lid and cook for exactly 15 minutes without lifting the lid.
Remove lid carefully, check that dumplings are cooked through with a toothpick. Ladle into bowls and garnish with additional parsley if desired.