Step 1

Combine the dashi, soy sauce, and mirin in a small saucepan. Place over medium heat. As soon as the dipping sauce comes to a boil, turn off the heat.

Step 2

Combine the yolks and water in a bowl, mixing until they’re incorporated, then add the ice cubes (the “wet” part of the batter). In another bowl or container, add the flour (the “dry” part of the batter).

Step 3

When you’re almost ready to cook the tempura, reheat dipping sauce over low heat. Grate the daikon on the coarsest side of a box grater. Squeeze out excess liquid and set aside. Grate the ginger finely and set aside. Keep the sauce warm while you prepare a tempura cooking station.

Step 4

To prepare a tempura cooking station, beside your burner, arrange the vegetables, a plate with the ½ cup of cake flour, and the wet and dry parts of the batter. Also, ready a tray lined with paper towels or newspaper to absorb the excess oil from the cooked vegetables, and the tools you’ll need: chopsticks, a metal strainer, and a candy thermometer, if you have one. Place a cooking vessel on the burner; use one with a uniform size to heat oil evenly, like a large cast-iron skillet or Dutch oven (don’t use a wok). Add the vegetable oil and sesame oil.

Step 5

Heat the oil to 360°F over high heat. When the oil has reached 360°F, prepare to cook the vegetables in batches. Be careful not to overfill the skillet, which will lower the cooking temperature; use, at most, half of the surface area of the oil to cook. While the tempura is cooking, check the oil temperature with a candy thermometer. Regulate the heat to maintain a constant 360°F oil temperature. If the oil is too hot, the tempura will burn; if too low, the tempura will come out soggy and greasy.

Step 6

When you’re ready to cook the tempura, quickly add the flour (the “dry”) to the liquid (the “wet”), in one shot. Hold 4 chopsticks together, the tips pointed down, like you’re grabbing a bottle. Stab at the batter with the chopsticks, mashing down again and again to combine the dry and wet parts. Do not stir; you barely want to mix the batter. Mix for about 30 seconds, or until the batter becomes loose and liquidy, with the consistency of heavy cream. It should be lumpy, with visible gobs of dry flour floating in the liquid, and with unmixed flour sticking to the sides of the bowl. Remember, if you overmix the batter, you’ll ruin it.

Step 7

Lightly dredge the vegetables in the reserved cake flour, then dip into the batter. Immediately lay the vegetables in the hot oil. Working in batches, deep-fry the harder vegetables like sweet potato, carrot, or lotus root first, for about 3 minutes, until the vegetables turn golden brown. Transfer the vegetables to the prepared tray to drain excess oil. Repeat with the other vegetables. Cook softer vegetables like asparagus, broccoli, and pumpkin for about 2 minutes. For shiso leaves, dredge only one side of the leaf with flour, and cook for about 1 minute.

Step 8

Serve the vegetable tempura with the grated daikon and ginger on the side of the warmed dipping sauce. When you’re ready to eat, add the daikon and ginger to the dipping sauce and dip the tempura into it.