Preheat the oven to 350 degrees.
In a skillet over medium high heat on the stove, melt the butter.
Add the onions and celery to the skillet with the butter, and saute until they begin to become tender.
Place the shredded chicken, minced garlic, Italian seasoning as well as salt and pepper to taste to the skillet, and stir to combine. Continue to cook for another minute.
Pour the heavy whipping cream and chicken broth into the skillet, and cook for a few more minutes until the mixture begins to thicken.
Transfer the chicken mixture into an even layer in the bottom of a casserole dish.
Mix together the ingredients for the dumplings until a dough has formed.
Roll the dough into small dumpling shaped balls, and mix them gently into the chicken mixture in the casserole dish.
Bake for 15-20 minutes, and let rest for several minutes before serving.