In a 10- to 12-quart pan, combine 1 cup soy sauce, brown sugar, 1/4 cup ginger, 6 cloves garlic, and 4 quarts water; mix well.
Remove giblets from chicken and reserve for other uses. Pull off and discard lumps of fat. Rinse bird well inside and out; pierce skin all over with a fork. Lay chicken breast down in brine; cover and chill at least 4 or up to 12 hours, turning bird several times.
Discard brine and rinse chicken thoroughly under cold running water, rubbing gently; pat dry. If desired, fold wing tips under first joint. Set bird breast up on a V-shaped rack in an 11- by 17-inch pan.
Starting at the neck, gently ease your fingers under skin to loosen it over breast. Push 1/4 cup chopped cilantro under skin and spread evenly over breast. Place cilantro sprigs in body cavity; add 2 tablespoons ginger and remaining 4 cloves garlic. Sprinkle chicken lightly with salt and pepper.
Roast in a 425° regular or convection oven for 30 minutes.
Meanwhile, in a large bowl, mix remaining 1/4 cup soy sauce, 2 tablespoons ginger, and 1/4 cup chopped cilantro with broth, vinegar, mirin, hoisin, and sesame oil. Rinse and drain shiitake mushrooms; trim and discard stems. Rinse and drain green onions; trim and discard ends. Cut off green tops and chop; also chop white bottoms. Mix mushrooms, chopped white parts of onions, and all but 1/2 cup chopped green tops with soy mixture. Lift out with a slotted spoon and distribute around chicken in pan; reserve soy mixture.
Continue to roast chicken, turning vegetables with a wide spatula after about 20 minutes, until a thermometer inserted through thickest part of breast to bone reaches 170°, or 180° through thickest part of thigh at joint, 3/4 to 1 1/4 hours longer.
Insert a carving fork into body cavity, piercing carcass; lift bird and tilt to drain juices into pan. Set chicken on a rimmed platter. With a slotted spoon, arrange vegetables around chicken. Let rest in a warm place about 15 minutes.
Meanwhile, skim and discard fat from pan. Add reserved soy mixture and stir often over high heat, scraping browned bits free, until reduced to 3/4 cup, about 10 to 12 minutes. Pour through a fine strainer into a small pitcher or bowl.
Sprinkle mushroom mixture with remaining 1/2 cup chopped green onion tops. Carve chicken and serve with vegetables and pan juices. Add salt and pepper to taste.