For the Broth: Place chicken in a large soup pot and cover with water.
Add onion, carrots, celery, garlic, salt, pepper, and nutmeg.
Cook over medium heat for about 45 minutes or until chicken is very tender.
Remove chicken to a platter and set aside to cool.
Meanwhile, bring chicken broth to a boil, then lower heat and reduce the broth to about 10 cups.
When chicken is cool enough to handle, chop into bite sized pieces; set aside.
For the dumplings: In a medium bowl, combine the flour, baking powder, salt and pepper; whisk to combine.
Cut the butter into the flour mixture with a fork or pastry blender and mix until crumbly.
Stir in cooled chicken broth and continue to blend until the dough forms a ball.
On a heavily floured work surface, roll out dough to about ¼ inch thickness.
Using a pizza cutter or sharp knife, cut the dumplings into 1 ½ to 2 inch squares.
Place dumplings on a floured plate and generously dust the tops of the dumplings with flour while piling them onto the plate to prevent sticking.
Finish the soup: Bring the finished broth to a rolling boil.
Drop the dumplings in one at a time, letting them sink into the broth.
Reduce heat to medium-high and cover with a tight fitting lid and cook the dumplings at a medium boil for about 20 minutes. (The soup should have thickened slightly into a thin “gravy” with the additional flour on the dumplings.)
After dumplings have cooked, stir in the half and half; heat to a low boil and continue to cook for an additional 5 minutes. (If soup is too thin, make a slurry by whisking together 4 tablespoons flour with 4 tablespoons water until smooth – stir in slurry a little at a time until the soup thickens to the desired consistency. Cook for 1 to 2 minutes after adding.)
Stir in the cooked chicken and season with salt and pepper to taste.