Combine the dashi, soy sauce, mirin, and sugar in a small saucepan and bring it to a boil. Then, lower the heat and let it simmer until the sugar is completely dissolved. Remove from the heat and set aside.
To Prepare the Ingredients
Follow these instructions to straighten the shrimp, so it looks gorgeous. Pat the shrimp dry and make sure the moisture is completely removed from the shrimp.
Cut all the vegetables (except the eggplant) ¼-inch thick. For the eggplant, cut off and discard the stem and calyx, then cut it in half lengthwise. With the cut side flat on the cutting board, cut the eggplant lengthwise into very thin slices (about ⅛ inch or 3 mm), being careful to leave the bottom tip intact by 1 inch (2.5 cm) so the slices stay connected. Then, gently press down on the slices to fan them out. Repeat with the other eggplant half.
To Prepare the Oil
In a medium-sized pot, heat 1½ inches to 2 inches (3-5 cm) of the oil to 350°F (180°C).
To Make the Tempura Batter
While the oil is heating up, start preparing the tempura batter. Add the egg and the iced water into a 2-cup measuring cup (or any bowl). Whisk the egg mixture vigorously and discard the foam on the surface.
Sift the flour into a large bowl. Slowly pour the egg mixture into the flour. Mix the batter, but do not overmix; it’s okay to leave some lumps in the batter. Keep the batter cold at all times (store it in the refrigerator if needed). Make the batter right before deep-frying to avoid activating the wheat gluten.
To Deep-Fry the Tempura
Check the oil temperature with a thermometer to make sure the oil is 350°F (180°C). You can also use wooden chopsticks to check; when you dip your chopsticks in the oil and see small bubbles forming, it’s ready for deep-frying. Please note that sweet potatoes and kabocha require a lower cooking temperature (320ºF/160℃). If you want to read more deep-frying tips, please read this post.
Deep-fry starting with the cleaner and less astringent ingredients. For example, the cooking order would be shiso first, followed by the mushrooms, eggplant, shrimp, sweet potatoes, and kabocha. Make sure your ingredients are dry before dipping them in the batter; if they’re wet, dry them with a paper towel first. While the tempura is frying, the moisture from the ingredients will evaporate and the tempura will become crispy. However, if the ingredients have extra moisture, the tempura will become soggy after deep-frying.
When the oil reaches the right temperature, dip one piece of vegetable or shrimp in the batter, let the excess drip off for a second or two, and very gently place it into the hot oil. Continue dipping and adding one piece at a time. For the shrimp, sprinkle some flour or potato starch (or cornstarch) over it before dipping to help the tempura batter adhere. For the shiso leaves, sprinkle a bit of sifted flour on the back of the leaf, dip only the back of the leaf into the batter, and deep-fry for 15 seconds. The flour acts as a glue and the batter tends to stay on the ingredients better.
Deep-fry the ingredients until golden brown. Do not crowd the pot because the oil temperature will drop quickly. Remember, your ingredients should take up no more than about half of the oil surface area at any one time.Here’s the rough cooking time for each of the ingredients: Shiso (350ºF/180ºC, 20-30 seconds), mushrooms (350ºF/180ºC, 1 min), eggplant (350ºF/180ºC, 1 min), shrimp (350ºF/180ºC, 2 minutes), sweet potatoes (320ºF/160℃, 3 mins), and kabocha (320ºF/160℃, 2-3 mins). Note that sweet potatoes and kabocha require a lower cooking temperature than the rest of the tempura ingredients.
Transfer the tempura to a wire rack or a plate lined with a paper towel to drain the excess oil.
Between batches, clean the oil by scooping up the crumbs (called tenkasu), which will burn and turn the oil darker if left in the pot.
Grate the daikon and squeeze the liquid out. Prepare 3-4 Tbsp of warm tentsuyu in individual small bowls and serve the grated daikon on the side.
Put 1 Tbsp of the grated daikon in the sauce and dip the tempura in the sauce to enjoy.
You can keep any leftovers in an airtight container and store them in the refrigerator for up to 2 days and in the freezer for 2 weeks. Reheat the tempura at 350ºF (180ºC) in the oven until warm and crisp.