Heat a saute pan or pot (if making larger portions) on medium heat. Once hot, add the oil. Saute the onion, carrots, celery, and garlic until vegetables just start to soften. Stir in the flour and cook until combined. Add the chicken broth, chicken, and thyme sprigs. Season with salt and pepper. Bring to a simmer to build flavor.
Cook the rice according to the directions on the package. Once tender season with salt and pepper to taste. Cover with a lid to keep warm until ready to serve.
For the dumplings: In a large bowl, whisk together flour, baking powder, garlic powder, chopped thyme, and salt. Make a well in the center of the flour mixture and mix in the milk a little at a time until a sticky dough ball forms. (If your dough seems too dry, you can add extra tablespoon(s) of milk until it is sticky and fluffy.)
Using a teaspoon, scoop the dough and drop directly into the simmering broth. Space them around the pot so they do not stick together. Cover with a lid, cook for about 10 to 15 minutes, gently stir the soup/dumplings (to check the dumplings cut one in half to make sure they are cooked through). (Add more broth as needed if the sauce is getting too thick) Taste and adjust the seasoning with salt and pepper if needed. Remove the thyme sprigs before serving.
Serve with rice and bread. Garnish with parsley.