Place the seaweed in a small bowl and cover with warm water. Stand for 10 minutes until softened. Drain. Squeeze the seaweed to remove excess water and julienne. Whisk the flour, bicarbonate of soda and salt in a large bowl. Whisk in the seaweed, eggs and tofu. Gradually add the soda water, until a smooth batter forms: it should be the consistency of a thick pancake batter. Refrigerate the batter until ready to cook.
For the lime mayonnaise, process the egg yolks and eggwhite, lime and salt in a food processor on high speed until combined. While the food processor is still running, add the grapeseed oil in a thin stream and process until emulsified and the mixture is thick. Chill and reserve.
Heat the vegetable oil in a large, heavy-based saucepan to 175°C (345°F) or until a cube of bread dropped into the oil turns brown in 20 seconds. Deep-fry tablespoon-size portions of the batter, in batches, turning occasionally, until they are golden and puffed (2–3 minutes on each side), then drain on paper towel. Take care, as the hot oil will spit.
Dot a serving plate with the lime mayonnaise and, using a pastry brush, generously brush the beignets with yuzukosho. Serve immediately.
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