Make the sauce by combining ginger, garlic, 1/2 cup water, soy sauce, brown sugar, rice vinegar, and red pepper flakes.
Combine sauce and chicken in the bowl of an Instant Pot. (Note: If you don't want to add the pot-in-pot rice, skip ahead to Step #5.)
Top it with a rack that is approved for use in the Instant Pot.
Combine rice and 1 cup of water in a bowl that is approved for use in the pressure cooker. Place the bowl with rice on top of rack.
Close and lock the lid. Set steam valve to Sealing.
Cook on manual / high pressure for 4 minutes.
When chicken and rice are done cooking, leave pressure on natural release for 10 minutes and then manually release any remaining pressure.
Carefully remove the bowl of rice and rack, leaving chicken in the bowl.
Turn on the pressure cooker’s saute function to normal / medium.
Meanwhile, whisk cornstarch and 2 Tbsp water together until smooth. Add cornstarch mixture, Hoisin sauce, and toasted sesame oil to chicken.
Simmer for 1 to 2 minutes until the sauce thickens. (Be careful not to cook any longer than a minute or two so that the chicken doesn’t overcook.)
Serve chicken and sauce over rice. Top with peanuts and chopped green onions.