1. Heat the oil in a 10-in. skillet over medium heat. Add the onion, mushrooms, celery and carrots and cook until the vegetables are tender, stirring occasionally. Remove the skillet from the heat.
2. Heat the butter in a 10-in. oven-safe skillet over medium heat. Stir in the flour. Gradually stir in the half-and-half and broth. Cook and stir until the mixture boils and thickens. Stir in the sherry, thyme, parsley and garlic powder. Season with the cayenne pepper, if desired.
3. Stir the turkey, chicken, onion mixture, peas, vermicelli and cheese in the skillet.
4. Heat the broiler. Broil 4 in. from the heat until the turkey mixture is hot and bubbling and the top is browned.