1. In a large pot, melt butter over medium heat. Sauté onion, carrots, and celery until softened. Sprinkle in the flour and stir to coat the vegetables.
2. Gradually whisk in the chicken broth, ensuring no lumps form. Bring to a simmer and add thyme, salt, and pepper.
3. Stir in the shredded chicken and heavy cream, letting the soup gently simmer.
4. In a bowl, mix flour, baking powder, and salt for the dumplings. Stir in melted butter and milk to form a sticky dough.
5. Drop spoonfuls of dough onto the simmering soup. Cover and cook for 15-20 minutes, or until the dumplings are puffed and cooked through.
6. Garnish with fresh parsley and serve warm.