Step 1

Adjust oven rack to middle position and heat oven to 450 degrees. Set wire rack in rimmed baking sheet lined with aluminum foil. Make 3 diagonal slashes through skin of each thigh with sharp knife (do not cut into meat). Brush chicken with 1 tablespoon vegetable oil. Lay chicken, skin side up, on half of prepared rack and roast for 20 minutes.

Step 2

Toss bell pepper and mushrooms in bowl with remaining 1 tablespoon vegetable oil, half of garlic, and half of ginger. Spread vegetables over empty side of rack and continue to roast for 10 minutes. Sprinkle snap peas over vegetables and continue to roast until chicken registers 165 degrees and vegetables start to brown, about 10 minutes.

Step 3

Remove sheet from oven. Adjust oven rack 8 inches from broiler element and heat broiler. Broil chicken and vegetables until well browned and registers 175 degrees, 3 to 5 minutes.

Step 4

While chicken and vegetables broil, combine mirin, soy sauce, water, sugar, cornstarch, pepper flakes, remaining garlic, and remaining ginger in bowl and microwave, whisking occasionally, until thickened, 3 to 5 minutes.

Step 5

Remove sheet from oven, brush chicken with 3 tablespoons of sauce, and let rest for 5 minutes. Transfer vegetables to clean bowl, toss with sesame oil, sesame seeds, and salt. Serve vegetables and chicken with remaining sauce.