Goulash or gulyas (= herdsmen; as in a dish cooked by such on the range) is the national dish of Hungary.
It is pronounced "GUL-YAS"  ("LY" in Hungarian is pronounced as a "Y").

The organoleptic distinction of goulash is the taste of heaps of paprika and onions.
Depending on the origin of the goulash recipe, various spices such as carraway seeds, cinnamon, dill or poppy seeds may be added.
A traditional goulash has a consistency between a stew and a soup, and is apparently never thickened with flour (it is thickened by only the ingredients).

This is my version giving a taste and consistency to my liking:

Ingredients

800 g Beef shank (diced into large pieces)
3 (or more) Large onions (sliced)
4 large cloves of garlic (diced)
2 tablespoons tomato puree
2 large carrots (sliced)
3 stalks of celery (sliced)
Some mushroom (sliced)
1 bay leaf
A good dash of ground pepper
Stock powder (chicken or beef)
2 - 4 heaped tablespoons paprika (or even more - only a minimal amount was used in the the cooked result in the pic above; the finished dish should have a red hue if enough paprika is used)
Starch suspension

Method

In a heavy bottomed pan (like a Dutch oven), sear the beef pieces. The greater the sear, the more the flavor which results in the goulash. Set aside.

Now fry the onion slices until translucent; add the garlic and fry only until the garlic is smelt.

Add the carrots and continue frying for a few minutes after which return the seared beef to the pan.

Add the tomato puree and continue frying.

Only now is paprika is now added (it is not fried at the beginning as this may change its taste).

Add ground pepper and stock powder to taste (add less than necessary at this stage and do final adjustment near serving time).

Add the bay leaf.

Add water to cover the beef.

Lid the pan and slow simmer for at least 3 hours (or less if you transfer the lot to a pressure cooker).
A slow cooker is an alternative to simmering in a pan.
Beef shank is a good cut for stews such as a goulash provided it is cooked long enough to break down the connective tissue into a gelatinous mouth feel. Other cuts without such tissue turns out "dry" and "wooden" on the tooth).

Add the sliced celery in the last hour of the cooking so that it does not turn mushy.

In the last minutes of the cooking, stir some starch in a suspension into the pan to thicken the broth.
You may not need to thicken with starch is you added as some do, diced potato.

Serve with your choice of carb: mashed potato (as above); pasta shells (as here with a beef casserole); even rice.
 

Boldog főzés!