Cook on high pressure for 10 minutes. Let the pressure release naturally (i.e. do nothing) for 10 minutes, and then turn the valve to release the remaining pressure.
Remove the whole chicken breasts from the Instant Pot and place them on a plate. Put the broccoli into the soup and seal the Instant Pot. Do not turn the Instant Pot on – the residual heat will cook the broccoli.
Meanwhile, shred the cooked chicken using two forks, or chop into bite-size pieces. Put the cut chicken back into the soup and stir.