Melt 3 tbsp butter in a large pot over medium heat. Add the diced onion and sliced celery and cook for 6 minutes until soft. Stir in the minced garlic for 30 seconds.

Pour in the 6 cups chicken broth and 1 cup whole milk. Add 1 tsp salt, 1/2 tsp pepper, and 1/2 tsp thyme. Bring to a simmer over medium-high heat, about 8 to 10 minutes, then add the shredded chicken.

Whisk together 2 cups flour, 1 tbsp baking powder, and 3/4 tsp salt. Stir in 3/4 cup whole milk and 3 tbsp melted butter until a shaggy dough forms. Let rest 5 minutes.

Roll the dough out on a floured surface to 1/8 inch thick and cut into 1-inch by 2-inch strips.

Drop the dumpling strips one at a time into the simmering broth. Reduce heat to medium-low and cook uncovered for 10 to 12 minutes, stirring gently every 2 to 3 minutes, until the broth thickens.

Ladle into wide bowls and finish with a crack of black pepper and a pinch of fresh parsley.