How is the name of this Hungarian food dish spelled?!

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Possibly kásás hús 'meat with cereal'? It's not the most common name for the dish; most people call it by its ingredients: rizses hús 'meat with rice'.

This explanation describes the stuffing in a cabbage roll. We call the cabbage Roll recipe "Hallishkas" Following is a recipe for unstuffed cabbage rolls which I like to make instead of the traditional stuffed ones.
Firstly I prepare the meat almost like meatballs except I add uncooked rice.
1 lb ground beef or chicken
1 egg
1/2 cup cooked rice
1/2 tsp salt
1/4 tsp pepper
1 tsp dry mustard(opt)
1 tsp dry parsley flakes(opt)
1/2 tsp granulated garlic powder
1/2 tsp granulated onion powder
1/4 cup breadcrumbs
1/4 cup water
Mix all ingredients and form into large meat balls
Fry meatballs in pan until brown on all sides. Remove and set aside. See recipe for Cabbage Sauce ingredients as follows:
1 Vidalia onion sliced
1/2 Cabbage sliced 1/2 inch slices pre-cooked in microwave for 10 minutes
1 large can whole or chopped tomatoes
1 can tomato paste and 1 paste can water
1/2 cup brown sugar more or less to taste
1/8 cup lemon juice or more to taste
In a Dutch oven or electric frying pan, in 2 tbsp Olive Oil fry first the onion then add pre-cooked cabbage then all the rest of the ingredients. Taste for a sweet and sour taste and adjust to your own taste. Place the meat balls on top of the sauce in the frying pan and continue cooking on medium-low temperature for about 1 hour, until done. Meatballs can be incorporated gently into sauce as they firm up during the cooking.
What you describe I feel is a similar taste of the tomatoes and ground meat with rice inside the meatballs. As for the Sweet and Sour flavour , one can leave that to ones own taste and change the final result by not using lemon juice and brown sugar..

I think, the food You are asking for is "tomato sauce" which is the exact translation of "Paradicsom szósz".

But the "kah-sha-soosh" is strange, I think, You heard something wrong, or somebody tried to explain the food as it's something like "Kása" OR "sauce" and You heard it Kah-Sha-Shoosh".

"Kahsah" could be "Kása", but it's a name of a different russian food, "shoosh" could be "szósz", which equals to sauce (this food sometimes referred as "paradicsom püré" - tomato puree). In this case what You heard could be the: "Pah"-"rah"[dicsom] shoosh".

EDIT: The below answer is the possible perfect solution for the "kah-shas-hoosh". (ká-sás-hús), but if the spelling is ok, then this means the "meat with rice", which is usually made with peas but not with tomato. It's possible, that this name was just given by a family or a restaurant for one of these dishes.

KASHASHOOSH!

Juli and AT are the best! I myself am Hungarian, but I would have never guessed! "Kásás hús" is the correct answer - it must be.