In a medium saucepan, bring the rice and the water to a boil. Cover and cook over low heat for 15 minutes, until the water is absorbed. Remove from the heat and let stand, covered, for 10 minutes. Scrape the rice into a bowl. Cover with a kitchen towel and let stand until cool enough to handle, about 30 minutes.
Meanwhile, heat the oil in a medium nonstick skillet. Add the walnuts and cook over high heat, stirring, until lightly toasted, about 3 minutes. Add the edamame, molasses and the 1 1/2 tablespoons of soy sauce and cook over moderately high heat, stirring, until sticky, about 5 minutes. Stir in the sesame seeds. Transfer to a bowl and let cool.
Set 1 nori sheet on a bamboo sushi mat. With lightly moistened hands, pat 2/3 cup of the sushi rice onto the nori in a rectangle that covers the lower two-thirds of the sheet, about 1/3 inch thick. Crush 2 rice grains in the empty corners to act as glue. Arrange 2 shiso leaves over the rice. In the center of the shiso, arrange a piece of daikon, 2 tablespoons of carrots and 2 tablespoons of the walnut-edamame mixture. Lift the end of the bamboo mat nearest you up and over, pressing to tuck the filling into a cylinder. Tightly roll up the fillings. Repeat to form the remaining 9 rolls. Cut each roll into 6 pieces and transfer to a platter. Serve with soy sauce.