Resolve the Mind's Desire trigger, copying it zero times.
Resolve the Eye of the Storm trigger, exiling Mind's Desire, copying Mind's Desire and Stolen Identity, and casting the Mind's Desire copy then the Stolen Identity copy, targeting Mirror of Fate, without paying their mana costs.
The Mind's Desire copy triggers, creating an additional Mind's Desire copy for each spell cast before it this turn.
Resolve those copies, exiling random cards from your library that you may play this turn.
Resolve the Stolen Identity copy, creating a token copy of Mirror of Fate.
Activate any Mirror of Fate by tapping and sacrificing it, exiling all cards from your library and putting Stolen Identity from exile on top of your library.
Resolve the remaining Mind's Desire copy, exiling Stolen Identity from your library and allowing you to cast it this turn.
Cast Stolen Identity from exile without paying its mana cost, choosing any target.
Eye of the Storm triggers, exiling Stolen Identity, copying Mind's Desire and Stolen Identity, and casting the Mind's Desire copy then the Stolen Identity copy, targeting Mirror of Fate, without paying their mana costs.
The Mind's Desire copy triggers, creating an additional Mind's Desire copy for each spell cast before it this turn.
Resolve these copies, failing to exile anything from your empty library.
Resolve the Stolen Identity copy, creating a token copy of Mirror of Fate.
Repeat from step 8.
Once you have infinite storm count, repeat the loop but put Brain Freeze on top of your library with a Mirror of Fate activation in step 8.
Once Mind's Desire has exiled Brain Freeze, cast Brain Freeze from exile without paying its mana cost.
Brain Freeze and Eye of the Strom each trigger.
Resolve Brain Freeze's trigger, creating any number of copies of itself targeting any number of players.