Heat olive oil in a large pot and brown both sides of chicken breasts, remove from pan (chicken does not have to be fully cooked yet)
Melt butter in pan and sauté onions, carrots, celery, garlic, Italian seasoning, and salt and pepper until fragrant
Sprinkle in flour, stirring and cooking for 1 minute to create a roux
Pour in chicken broth and heavy cream and bring to a boil
Add chicken back to pot, lower heat, and simmer 15 minutes
In a bowl, combine all dumpling ingredients and mix together
Remove chicken from pot, shred, and add back to pot
Drop dumpling dough by spoonfuls into pot and cover with lid
Simmer 10-15 minutes
Serve with fresh parsley
