Andalucia and the Ebro delta (just to the north of Valencia in Tarragona) together produce 50% of Spain's rice, but Valencia (producing a further 18%) has become closely associated with rice dishes made from the short grain arborio rice grown in Spain. The most famous being Paella (pie-ay-ah), which has two styles, Valencian being a different type, without a sofrito. Note that it is considered impolite to arrive late for a paella and when a waiter brings the plates for the main course its probably time to finish the starters quickly. When the paella is ready - it is ready!

Paella Mixta ¹
Soften one Spanish  onion and a few cloves of garlic in olive oil in a wide pan, add four skinned plum tomatoes and cook down to a sofrito. Add some pieces of chopped chicken²,  as well as a few saffron threads. When the chicken is cooked add a cup of arborio rice and some water. When rice is almost soft add a variety of seafood in time to be cooked when the rice is ready. Prawns, clams, squid and mussels make a good choice. Take the pan to the table decorated with lemon wedges and some "specimen" seafood such as crayfish or large prawns you have cooked in the oil before starting the paella.
 

1 "Valencia" paella is meat not fish based, see below
2 Many purists do not believe in mixing seafood and meat, so you may want to leave this out, even though it is common in Spain and may have originated in the wish of non christians to be seen to be eating "christian" food at the time of the Inquisition.
 

Paella cookbook

Arroz a banda
Rice and sofrito flavoured with the pan juices and fish frames and shells from fish and seafood used in other dishes. Some authorities claim it is served with the actual fish and seafood in a separate bowl. I ordered it in a locals bar in the middle of the Valencian rice paddies and it came just as the rice. Perhaps the home cook or expensive restaurant would serve with the seafood. Anyway, my "take" on this dish is to fry the rice and garlic, along with a little chopped tomato and onion, then add fish/seafood stock of good quality, flavoured with saffron, simmer for about 20 minutes until the stock is absorbed.

Paella Valenciana
Meat and beans replace the seafood of the marisco version (it is worth remembering that paella may contain almost anything).
There is no sofrito in this version, just tomatoes.
Beans, both green (french beans) and white (garrofó)  with rabbit or chicken and possibly snails; rosemary, saffron and sweet paprika (pimenton dulce).
José Martínez's authentic recipe

My version of "Fideua" (for two) using any seafood and fish pieces to hand. (Clams, prawns and pieces of monkfish would be fine)
Make a rich fish stock from fish frames and seafood shells. Strain, reduce and add saffron.
Roast three red peppers (30 minutes) until soft, skin and slice, discarding seeds.
Fry fresh prawns and pieces of boned fish in olive oil, set aside.
Make and boil one portion of thin pasta like spaghetti, strain and cut into short lengths.
Cook any bivalves in the stock, add the fish and seafood with the oil along with any precooked seafood and the peppers, add the pasta and then thicken with a picada made from pounding garlic and parsley. Serve.

Jambalaya
The Louisiana dish Jambalaya is almost certainly a descendant of Paella made with local ingredients. The source of the name is less certain:-
It may be Jamon- Paella (ham- paella) or it may come from the French "jambon".
One source suggests it is Jamb(on), the African[1] word "ya", meaning rice, with the Acadian [Cajan] "a la" in between. But this seems to assume that the current spelling can be relied on, (an 1880s recipe refers to "jumberlie" and spelling was certainly "jumbalaia" before the current one). 
Jumbalaya replaces the sofrito with a saute of celery, onion and (bell) pepper, "chaurice" sausage takes the place of "chorizo", ham, possibly chicken, cayenne and paprika are added along with lots of tomato. The rice when added is softened with chicken stock, the dish being finished with prawns. Like Paella, it is a very variable dish.
[1] no specific language quoted 
 

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