In a pot, combine dashi, mirin, and soy sauce, and bring it to a boil. Once boiling, let it simmer for about 30 seconds, then remove from the heat. Transfer the broth to a heatproof container and let it cool to room temperature (chilling in the refrigerator is ideal).
Cut the eggplants in half lengthwise, removing the stems first. Make shallow cuts at short, even intervals on the skin. If the eggplants you are using are larger than the pot for deep-frying, cut them horizontally into halves or thirds as well. (Since eggplants brown quickly after cutting, it is best to do this step just before deep-frying in the next step.)
Heat oil in a pot to 340℉ (170℃). Once the oil is hot, carefully add the eggplants one at a time, skin side down. Deep-fry them for 1 minute.Be careful not to add too many pieces at once, as this can cause the oil temperature to drop significantly. The eggplants should occupy no more than about two-thirds of the oil’s surface area. Flip the eggplants over and continue frying until they become soft enough to indent easily when pinched with chopsticks or tongs (about 1 minute, depending on the size of the eggplants you use).
Remove the eggplants from the oil and let them drain on a wire rack. While still hot, transfer them to the container with the broth, skin side up. Repeat the frying and soaking process (steps 3 to 5) until all the eggplants are soaked. Let the eggplants soak in the container at room temperature or in the refrigerator for at least an hour to allow the flavors to meld.
They are delicious on their own, but you can also serve them with garnishes, such as grated daikon radish, grated ginger, shredded shiso leaves, and chopped green onions for a refreshing touch, if desired.