To make the dipping sauce: Bring 1 cup of water to a boil and add the dashi. Boil for 3 minutes. Remove from the heat and add the remaining ingredients. Let cool and serve at room temperature.
In a 2-3 quart pot set over medium-high heat, heat 2 inches of oil to 360º.
To make the batter: Combine the egg and salt in a medium bowl and beat with a fork until mixed. Add the club soda and stir gently to mix. Sift the flour and cornstarch into the egg mixture and, using chopsticks or the handle of a wooden spoon, stir briefly to mix. Do not overmix. There will be lumps. It should be the consistency of heavy cream.
To fry the tempura: Working with one type of food at a time, dip the vegetables, shrimp, or scallops in the batter one at a time, letting the excess batter fall back into the bowl. Carefully slide them into the hot oil. Work fast and fry no more than 6 or 7 pieces at a time to prevent the oil from plunging in temperature.
Turn the pieces when they are slightly golden on the bottom, about 1 minute. Fry on the second side for about 30 seconds to 1 minute and carefully remove with a spider (an Asian-style slotted spoon) or slotted spoon and drain on paper towels.
Here are some approximate frying times:.
Zucchini = 1 1/2 minutes.
Yellow squash = 1 1/2 minutes.
Sweet potato = 2 minutes.
Broccoli florets = 1 1/2 minutes.
Small red onion = 1 1/2 minutes.
Small mushrooms = 1 1/2 minutes.
Shrimp = 1 1/2 to 2 minutes.
Scallops = 1 1/2 to 2 minutes.
Return the oil to 360º and carefully add another 6 or 7 pieces of tempura.
Fry the remaining ingredients in the same manner.
Serve the tempura hot with the dipping sauce, or with salt and freshly squeezed lemon. Grated daikon should be served alongside the fried vegetables. It can be added to the dipping sauce or on top of the vegetables.
Variation: Other vegetables to try are carrots, asparagus, and green beans. Cook them first in boiling water for about 1 minute, then put them in an ice bath to stop the cooking. Line up 4 or 5 carrots, asparagus, or green beans, side by side, and run a wooden skewer through them to connect. Dip them in the batter and fry them, then remove the skewer after frying. Other seafood possibilities include cod, crab and squid.
Make ahead: The dipping sauce can be kept for up to 1 week in the refrigerator.