How to Make It
Make the sushi rice In a medium saucepan, combine the rice with 1 1/2 cups of water and bring to a simmer. Reduce the heat to low, cover and cook until the water is absorbed and the rice is tender, about 10 minutes. Remove the pan from the heat.
Meanwhile, in a small saucepan, combine the vinegar with the mirin and sugar. Bring to a simmer and cook, swirling the pan, until the sugar dissolves, about 2 minutes. Fold into the cooked rice and season with salt.
Make the spicy mayonnaise In a small bowl, combine the mayonnaise with the Sriracha and lemon juice and stir until smooth.
Make the rolls Preheat a grill or the broiler. Carefully cut the crab legs lengthwise in half and brush with the butter. Grill over moderately high heat, cut side toward the heat, for 2 minutes. Turn the crab legs and grill until cooked through, 5 to 7 minutes. Transfer to a platter and let cool sightly. Remove the meat from the shells; discard the shells.
Lay 1 sheet of soy paper on a sushi mat. Using moist hands, pat 2 to 3 tablespoons of the rice in a layer on the sheet, leaving a 1/4-inch border. Spoon some of the cooked crab in a strip down the center of the rice and drizzle with the mayonnaise. Lift the end of the bamboo mat nearest you up and over, pressing to tuck the rice and crab into a cylinder. Tightly roll up the fillings in the soy paper. Repeat to form the remaining 7 rolls. Cut each roll into 6 pieces and transfer to a platter. Serve warm or cool with more spicy mayonnaise.
King crab legs are most often sold cooked, so be aware when purchasing them cooked all you have to do is thaw and reheat them. Your fishmonger may sell them already split, or you can ask to have them split, which makes shelling them easier.