Place Basic Japanese White Rice in a bowl. Combine vinegar, sugar, and salt; sprinkle over rice, tossing gently with a wooden spoon.
Combine shiitake mushrooms and the next 4 ingredients (through mirin) in a small bowl; set aside.
Cut off top quarter of each nori sheet along short end. Place 1 nori sheet, shiny side down, on a sushi mat covered with plastic wrap, with the long end toward you. Pat about 3/4 cup rice mixture evenly over nori with moist hands, leaving a 1-inch border on 1 long end of nori. Sprinkle about 3 tablespoons mushroom mixture over rice. Lift edge of nori closest to you; fold over filling. Lift bottom edge of sushi mat; roll toward top edge, pressing firmly on sushi roll. Continue rolling to top edge; press mat to seal sushi roll. Let rest, seam side down, 5 minutes. Slice about 1/2-inch from each end of roll; discard trimmings. Slice roll crosswise into 5 pieces. Repeat procedure with remaining nori, rice, and mushroom mixture. Serve with Ponzu Sauce.