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Step 1
Place the cut cucumbers in a mixing bowl and toss with the salt. Let sit 5 minutes, then rinse thoroughly. Pat dry. Return to a clean and dry mixing bowl and toss in the mirin, chili, and sugar. Cover and place in fridge until ready to use. Cucumbers can be made several hours in advance.
Step 2
First, prepare the glaze. In a small pot add the sake, mirin, sugar, and crushed pepper. Heat over medium-low, whisking regularly, until the sugar is dissolved. Turn off heat and add the miso. Whisk until smooth, then set aside until ready to use. The glaze can be made a day in advance and stored in the fridge.
Step 3
To make the eggplant, heat a large skillet or grill pan to medium-high heat. Brush the eggplants with the oil and place cut side down on the hot skillet. Cook for 3-4 minutes until well browned and charred in spots. Rotate 45º halfway through if using a grill pan for those nice crosshatch marks. Flip eggplant over and grill/cook skin-side down for an additional 3-4 minutes until grill marks appear or skin is charred in places. Place cooked eggplant cut side up on a foil lined baking tray.
Step 4
When ready to make the tacos, turn your oven to broil and place a rack about 6" from the top burner. Let the oven saturate with heat for about 10 minutes (this is a great time to prepare your tortillas & the garnishes). Brush or spoon plenty of miso-glaze (dengaku) over the cut sides of the eggplants. There should be some leftover glaze.
Step 5
Broil the eggplants ~3-5 minutes until the dengaku glaze is hot and bubbly. Remove from oven and serve as quickly as possible.
Step 6
Cut the eggplant to fit into the tortillas. Spoon a bit of extra dengaku onto a warm tortilla. Add two or three pieces of eggplant. Top with the marinated cucumber and garnish with toasted sesame seeds and green onions. Enjoy!