Cooking Tips – Why Fry Onions and Garlic Before Adding Other Ingredients?

Penelope Casas' The Foods and Wines of Spain explains that

Paella is a word that has come worldwide to mean a Spanish rice dish with a variety of seafood and usually some chicken. However, the word originally referred only to the pan in which the food was cooked--the paella or paellera, from the Latin word for pan, patella. Paellas actually come in endless varieties, depending on the chef and on regional specialties.

She emphasizes the technique more than traditional ingredients (which she notes that no two Spaniards will agree on), but includes recipes for a number of different rice dishes from many regions, all prepared in basically the same manner.

Interestingly, her Paella a la Valenciana (Tradicional) actually doesn't call for saffron (it does call for paprika). The meats are snails and rabbit, and she does call for an onion, but it's only used to steep for a while in the broth, and later discarded. She includes a single tomato which is cooked down with green peppers and garlic. Most of her other paella recipes include onion in this step, but it is notably absent from this recipe. She also calls for lima beans and "wide, flat string beans", and serve the dish with scallions on the side.

According to Wikipedia,

the preparation of a wat begins with chopped onions slow cooked, without any fat or oil, in a dry skillet or pot until much of their moisture has been driven away. Fat (usually niter kibbeh) is then added, often in quantities that might seem excessive by modern Western standards, and the onions and other aromatics are sautéed before the addition of other ingredients. This method causes the onions to break down and thicken the stew.