Combine the lemon, parsley, garlic, oil and salt in a blender until mostly smooth.
Toss the chicken with the gremolata and marinate overnight or for at least 4 hours.
Preheat the oven to 400°F.
In a medium saucepan, heat the soy sauce, ½ cup water, sugar, scallions, garlic, sake, dried shiitakes, and ginger. When the mixture reaches a boil, use a strainer to remove the vegetables. Simmer for 20 minutes.
In a small bowl, mix together the cornstarch and 1 tablespoon water. Add the slurry to the sauce and return to a boil. Remove from heat.
Remove the chicken from the marinade, discard marinade and season chicken with salt and pepper. Roast on a baking sheet until cooked through, about 15-20 minutes. Remove from the oven and brush with teriyaki glaze.
On one baking sheet, toss the mushrooms with the bacon, onion, 1 tablespoon olive oil, salt, and pepper. Roast for 15 minutes, until the mushrooms and bacon are both crisp.
On a second baking sheet, toss the brussels sprouts with 1 tablespoon olive oil and a big pinch of salt and pepper. Roast for 11 minutes, or until crisp.
Serve the chicken alongside roasted vegetables.