Whisk the soy sauce, lemon zest and juice, and the sesame oil together in a small bowl. Add the scallion whites to the sauce.
Mix the scallion greens with the ginger in another small bowl.
Lay the sole fillets on the work surface, skin-side up (look for the side with the herring bone pattern). Cut the fillets lengthwise along the natural seam that runs down the center of each piece. Lightly season the skin-side of the fish with salt and pepper. Then scatter the scallions and ginger on top. Starting from the narrow tail end, roll up each piece of fish into a tight spiral with the scallion on the inside. Secure with a toothpick if desired.
Pour an inch or more of water in a wok or skillet and bring to a boil over medium-high heat. Lay the Napa leaves in a bamboo or collapsible steamer. Stand the fish rolls on the Napa, and scatter the shiitake mushrooms and sliced carrot around. Set the steamer over the water, cover, and cook the fish until it is barely cooked through, about 6 minutes. Turn off the heat and leave the fish covered to finish cooking in the residual heat of the steamer, about 5 minutes more.
Divide the Napa, sole, shiitakes, and carrots among 4 plates and drizzle with the sauce. Serve.
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