On a 12-inch skillet, melt butter (4 tablespoons) over medium heat. Add onion (1/2 cup), red bell pepper (1/4 cup), celery (2 stalks), and carrots (1) then cook, stirring frequently, until the vegetables are very tender, about 8 minutes.
Stir the mushrooms (8 ounces), thyme leaves (2 teaspoons), 1 teaspoon salt, and 1/2 teaspoon black pepper into the skillet and continue to cook, stirring often, until the mushrooms are tender, about 3-5 minutes.
Sprinkle flour (1/4 cup) over cooked vegetables then stir until vegetables are evenly coated. Continue to cook, stirring constantly, for 1-2 minutes or so to cook out flour taste.
Slowly stir in the turkey or chicken stock (1 cup), stirring down to the bottom of the skillet to lift up any brown bits. Pour in heavy cream (3/4 to 1 cup) and simmer, stirring often, until sauce thickens, about 3-5 minutes.
Stir in the turkey (2 cups), green peas (1 cup), and sherry (2 tablespoons). Cook on low until turkey is heated through. Taste and adjust salt and pepper. Sprinkle with fresh parsley (1 tablespoon) and serve over rice, biscuits, or buttered noodles.