Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Heat sesame oil in the pot and add onion. Saute, stirring occasionally, until translucent, about 2 minutes.
Add broccoli, garlic, red pepper flakes, garlic salt, ginger, and orange zest. Cook and stir until fragrant, about 1 minute. Pour in orange juice, tamari, chili sauce, and honey. Stir in chicken. Select high pressure according to manufacturer's instructions; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Meanwhile, whisk cornstarch with chicken broth until dissolved.
Pull chicken and vegetables out of the sauce using a large slotted spoon. Place pressure cooker back on Saute mode. Cook until sauce starts bubbling; add cornstarch mixture. Let sit for 1 minute, stir, and turn pressure cooker off.
Stir aji mirin into the sauce. Add chicken and vegetables back in.
