In a large pot, bring salted water to a boil. Add the gnocchi and cook according to package instructions until they float to the top. Drain and set aside.
In the same pot, over medium heat, combine the shredded chicken, cream cheese, chicken broth, and heavy cream. Stir until the cream cheese is fully melted and everything is well incorporated.
Add the garlic powder, onion powder, Italian seasoning, salt, and pepper to the creamy mixture. Stir and let simmer for about 5 minutes.
Gradually stir in the shredded cheddar cheese until melted and the sauce is creamy.
Fold the cooked gnocchi into the creamy chicken sauce, ensuring they are well coated. Let simmer for an additional 2-3 minutes.
Taste and adjust seasonings as necessary.
Serve hot, garnished with sliced green onions and fresh parsley.