In a large pot, brown Chicken thighs over medium-high heat. Remove chicken and set aside.
Add Onion, Carrots, and Celery to the pot and sauté for 5-7 minutes, until softened. Add Garlic and cook for 1 minute more.
Return Chicken to the pot. Add Chicken broth, Bay leaf, Salt, Pepper, and Thyme. Bring to a boil, then reduce heat and simmer for 75-90 minutes, or until chicken is very tender.
Remove chicken from pot and let cool. Shred the chicken and discard the skin and bones.
Prepare the Knoephla Dough: In a bowl, combine Flour, Egg, Milk, Salt, and Nutmeg. Mix until a shaggy dough forms. Knead lightly for 3-4 minutes.
Using a knife or bench scraper, cut small, irregular pieces of dough (knoephla) and drop them into the simmering broth.
Cook the knoephla for 10-15 minutes, or until they are tender and have puffed up.
Return the shredded Chicken to the pot. Stir in Heavy cream and heat through. Do not boil.
Remove Bay leaf before serving. Garnish with Parsley.