In a Dutch oven or stock pot, melt butter over medium-high heat until foaming. Add mushrooms, onion, carrots, celery, Morton's Nature Seasoning, and poultry seasoning. Cook, stirring occasionally, until the vegetables have softened and released most of their liquid, about 5 to 7 minutes.
Stir in flour and cook until heated through, about 1 to 2 minutes. Whisk in one cup of broth until no lumps of flour remain.
Stir in remaining broth, chicken base, Kitchen Bouquet seasoning, chicken, and cooked wild rice. Heat until barely simmering, about 180 degrees.
Stir in half and half and return to 180 degrees (do not boil). Season to taste with salt and pepper (I like 1/2 teaspoon salt and 1/4 teaspoon pepper) and garnish with fresh parsley. Or, transfer to a slow cooker and keep warm.