Soak shiitake mushrooms until soft, about 2 hours. Drain, remove and discard stems, and slice thinly.
Heat oil over medium heat, add mushrooms, then carrots, and toss with a small pinch of salt. Stir in mirin or cooking wine and sauté briefly. Add scallions and sauté for about 5 minutes more. Lower flame, add soy sauce and ginger, toss, and add rice.
Break up any clumps of rice, mix thoroughly, cover, and cook 1-2 minutes more.
In a large bowl, toss carrots, cabbage, and bean sprouts; add kelp powder and cayenne, mixing thoroughly. Cover vegetables with a plate that fits down into the bowl and place a weight on top of the plate. Refrigerate for 6 hours or overnight.
Drain off liquid and toss vegetables with sesame oil, soy sauce, lemon juice, and parsley. Garnish with shredded nori on top.