Marinate chicken in Italian dressing and Greek seasoning for a minimum of 30 minutes.
Place chicken in a 23 x 33cm baking dish. Sprinkle top with additional Greek seasoning, if desired, and bake in preheated oven for approximately 25 minutes, or until no longer pink in centre and juices run clear.
Shortly before chicken is done, melt butter in a frypan over medium-high heat until bubbling. Pour in wine, Worcestershire sauce and garlic salt, then bring to a boil. Stir in mushrooms. Reduce to a simmer, cover and cook until mushrooms are tender, about 3 to 5 minutes. Adjust seasoning with salt as needed.
Remove chicken from the oven. Sprinkle chilli slices on top of each breast, then top with a slice of cheese and a sprinkle of dill. Return to the oven until cheese has melted.
Remove chicken from the oven, top with mushrooms and their pan juices and serve.