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1
Bring a pot of water to the boil. Add the abura-age pouches and boil for 2 minutes (abura-kiri). Drain and, when cool enough to handle, press each pouch firmly between your palms to expel the frying oil. The pressed pouches will be visibly drier and firmer.
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2
Combine the dashi, soy sauce, mirin, sake, and sugar in a wide saucepan. Add the drained, pressed abura-age pouches in a single layer. Bring to a gentle simmer and cook, turning the pouches once, until all the simmering liquid has been fully absorbed into the tofu. This is where the dish lives or dies: insufficient simmering leaves the tofu under-flavoured and structurally wet; fully absorbed liquid produces the characteristically sweet, glossy, saturated pouch. Remove from heat and allow to cool completely.
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3
Fold the toasted sesame seeds through the cooled sushi rice. Working with one pouch at a time, insert a chopstick gently into the slit edge and work it slowly inward to open the pocket without tearing. Then ease fingers in carefully to fully open the interior. The pouch should yield without resistance once the tofu has cooled.
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4
Take a portion of sushi rice sufficient to fill the pouch two-thirds to three-quarters full. Shape lightly into an oval and tuck it into the pocket. The pouch should close naturally over the rice without forcing. Over-filled pouches will not close and will tear under pressure. Fold the open edge neatly inward to seal, and place the pouch seam-side down on a tray. Repeat with remaining pouches.
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5
For the Hiroshima inverted (Tōdai) style, place the rice ball inside with the folded edge at the base, then invert the pouch so the rice is exposed at the open top. Arrange on a platter. The finished inari sushi may be held at room temperature for up to 4–6 hours.