Heat ¼ cup olive oil in a Dutch oven or stock pot to medium heat. Add onion, celery and carrots and saute 3-4 minutes, until starting to soften. Add chicken and saute 3-4 minutes, until browned.
Stir in spinach and garlic and saute 1-2 minutes, until wilted. Stir in Italian seasoning, poultry seasoning, salt, black pepper and cayenne. Add additional 2 tablespoons of oil and turn heat to medium-high.
Stir in flour and allow to cook 1-2 minutes, stirring constantly. Stir in chicken stock and evaporated milk and bring to a low boil. Add gnocchi and cook on a simmer 4-5 minutes, until gnocchi is tender.
Remove pot from heat and stir in Worcestershire sauce and ¼ cup Parmesan cheese. Taste and adjust seasoning, if necessary. Serve with remaining shaved Parmesan.