Start by melting butter in a large pot over medium heat. Add carrots, celery, mushrooms, and onion, then cook until tender and fragrant. Stir occasionally to ensure even cooking and prevent burning.
Mix in minced garlic, poultry seasoning, and thyme. Cook for a minute or two until everything smells aromatic. This step enhances the depth of flavor in the base.
Sprinkle flour over the vegetables and stir well. Let it cook briefly to remove the raw flour taste. This will help thicken the sauce later.
Slowly pour in chicken stock and milk while stirring to avoid lumps. Once smooth, add the gnocchi and bring to a gentle simmer. Let it cook until the gnocchi becomes soft and plump.
Stir in shredded chicken and frozen peas. Let everything heat through and blend together. Taste and adjust seasoning if needed before serving.