Position a rack in the center of the oven and heat the oven to 400°F. In a large bowl, toss the mushrooms with 1 Tbs. of the sesame oil. Arrange the mushrooms in a single layer on a rimmed baking sheet and roast until softened, 10 to 15 min. When cool enough to handle, slice the mushrooms into 1/4-inch slices and return them to the bowl.
Meanwhile, in a small bowl, whisk the remaining 1/2 Tbs. sesame oil with the tamari (or soy sauce), mirin, rice vinegar, and ginger. Set aside 1/3 cup of this mixture and transfer the rest to a small saucepan. Bring to a boil over high heat. Add the cornstarch-water mixture and cook, stirring, until thickened, about 30 seconds. Remove from the heat.
Line a 9x13-inch baking dish with foil. Arrange the salmon portions in the dish, skin side down and evenly spaced. Using a pastry brush, thickly dab the tops and sides of the salmon with the warm glaze. Use all of the glaze and don’t worry if some of it slides off of the fish. Bake until the salmon is cooked to your liking, about 10 min. for medium rare; 12 min. to medium; 14 minutes for medium well. (Cut into the thickest part of a fillet to check.) While the salmon cooks, add the red pepper, scallions, and reserved soy mixture to the mushrooms. Toss to combine and season to taste with pepper.
Drizzle the fish with any glaze that has pooled in the baking dish and serve topped with the mushroom salad.