Bring some water to boil. Add sheep hearts and allow them to turn whitish in colour. Remove any blood with the tip of a knife, then wash and dry the hearts. Fry in oil over medium heat on all sides for a few minutes.
Peel and thinly slice the onion. Wash and peel the carrot, then cut into thin, round slices. Wash and finely chop the herbs.
Add onion, carrot, herbs, salt, and black pepper to hearts. Follow with a cup of hot water and cook over low heat for about 40 minutes. A bit of juice should be left when cooking is over. Allow the hearts to cool.
Cut hearts length-wise taking care not to separate the two parts. Wash mushrooms and slice. Fry mushrooms in butter for about 10 minutes, while adding some salt and black pepper. Add mushrooms to the sauce prepared earlier and mix well.
Pour some of this sauce inside each heart and over them. Close the hearts to return them to original shape. Sprinkle grated cheddar cheese on top and serve with Iranian or middle-western bread.