The recipes for this on websites vary a lot - quite a few involve self raising flour, or baking powder added to plain flour; others recommend cornflower mixed in with it, or even potato starch. The matter of using an egg (or just yolk) is not even settled. The only universal thing is that the water used must be ice cold, and you do not want an over-mixed, smooth batter - lumps are good.
In any event, I found that plain flour, mixed with an equal quantity of iced water containing a lightly beaten whole egg, worked well. And one cup of flour and one of water makes quite a lot of batter. (Actually, I think I added a bit more water - I don't like thick batter. But it basically seems hard to go wrong (as long as the oil temperature is pretty high too.)
As for the dipping sauce - 1 cup of dashi (powdered stock type, of course); 1/4 cup each of mirin and soy sauce, plus a couple of teaspoons of sugar, all heated in a saucepan and cooled a bit for serving, worked well.
The history of tempura as a Japanese mainstay is interesting. As the Kikkoman company's website explains:
China, which has long influenced Japan, has traditions rich in culinary techniques based on the use of oil. In fact, written Chinese includes an array of characters used to distinguish different types of frying, such as quick-frying over high heat, searing at low heat, and so on.
Yet Japan was unaffected by this particular culinary aspect of China: early Japanese cooking was more strongly influenced by the injunction against eating meat that arrived with the introduction of Buddhism in the sixth century. This meat-eating taboo came to Japan by way of China, but Buddhism was not the state religion of China, nor was it closely associated with the ruling classes, as it was in Japan. Pig lard was used to prepare some dishes in China, but pork fat was unavailable in Japan, once the eating of pork was prohibited. Vegetable oils were obtainable here, but they were used mainly as fuel for illumination and their quantity was limited; thus the use of oil in cooking was slow to catch on.
Tempura most likely made its first appearance in Japan via Spanish and Portuguese missionaries and traders, who introduced deep-frying in oil during the latter half of the sixteenth century. Gradually, the type of cooking we now know as tempura became firmly established during the eighteenth century. As if to endorse this history, I have encountered a deep-fried squid dish in Portugal. And to my surprise, I enjoyed something called “fritters” —deep-fried seafood or vegetables—which had an uncanny resemblance to tempura in Malacca in Malaysia. Malacca is a bustling coastal port where the descendants of Portuguese colonists, who arrived during the early sixteenth century, pursue fishing and other trades while conducting their lives in the local vernacular, a dialect of Portuguese....
What was early tempura like? The oldest extant records, dating from the late seventeenth century, indicate that it consisted of balls made of a paste of thrush meat, shrimp and ground walnuts, which were deep-fried in oil, then covered with a sauce thickened with kuzu (a perennial of the bean family) starch. No batter coating seems to have been applied.
In the mid-eighteenth century there are records of deep-frying with a coating, apparently fish dusted with flour or root vegetables like burdock, lotus and taro dipped in a thin mixture of flour, soy sauce and water. Considerable innovations then followed, creating the tempura we know today: the production of vegetable oil increased and its price stabilized, making it possible to use generous amounts in cooking; soy sauce manufacture became an established industry, and this seasoning became more widely available; it was also during this time that bonito-flake stock was more commonly used.
During the Edo period, tempura-style cooking first became popular at movable outdoor stalls. In those days, Edo was built entirely of wooden structures, and so was extremely vulnerable to fire. Cooking outdoors rather than in houses was encouraged, and outdoor stalls serving foods like tempura were very popular. Like sushi, tempura flourished as a snack enjoyed by the common townspeople, and went on to become an essential element in the “flavor hierarchy” of Japanese cuisine.Thus ends today's culinary notes...